Are these beliefs sufficient for salvation?

Here is the disagreement in interpretation between us.
When we are under grace, as in walking in the Spirit we fulfil the law through love.

You are arguing Paul is suggesting if we sin under grace it is not sin. This is not what Paul
is saying. He talks about trying to justify ourselves under the law, by following its principles,
ie circumcision, but you then would have to be completely a jew, and Jesus would mean nothing.

1 Therefore, there is now no condemnation for those who are in Christ Jesus, ....
4 .... who do not live according to the sinful nature but according to the Spirit.
Rom 8

9 You, however, are controlled not by the sinful nature but by the Spirit, if the
Spirit of God lives in you. And if anyone does not have the Spirit of Christ,
he does not belong to Christ.
Rom 8

We are slaves to righteousness, not sin. We are controlled by the Spirit of God,
not the sinful nature.

One has to be careful how you interpret these ideas, because in taking Pauls
emphasis on freedom, as in freedom not to be following all the rules of Moses,
we are still bound by the law of the Spirit. But this is not through legalism but
through our hearts walking in love.

Slaves to righteousness are not slaves to sin and do its bidding.

16 Don't you know that when you offer yourselves to someone to obey him as slaves,
you are slaves to the one whom you obey--whether you are slaves to sin, which leads
to death, or to obedience, which leads to righteousness?
17 But thanks be to God that, though you used to be slaves to sin, you wholeheartedly
obeyed the form of teaching to which you were entrusted.
18 You have been set free from sin and have become slaves to righteousness
Rom 6

I thought Romans 5:13 is clear enough? Seems its not clear to you. If you do X, where X can mean any wrong act of your choice, it is still a sin. so I agree with you that it is sin.

But the point is, you cannot be imputed/charged with that sin in the eyes of God, because in his eyes, believers are not under any law regarding X.

Let me give a simple analogy. Do you know why you cannot be charged with a crime of "having more than 5 books" in many countries?

ABC's of salvation
Admit you're a sinner in need of salvation.
Believe upon the Lord Jesus Christ and the gospel of His death, burial and resurrection for sins.
Call upon Jesus Christ to be your Savior or your sins.

Taking one verse which says something possibly in one context which does not match
everything else is not how scripture works or the Lord for that matter.

We walk in love because that is our heart in Christ. And in walking in love, we fulfil
the law and are no long lawbreakers or under the law. Paul is conveying the law is
only about identifying failure, it does not guide us into walking with God.

John puts it simply as people of God we cannot continue in sin, because it goes against
who we are. Once you begin to see what evil is things change, and what we are in Christ.
Christ did not come so that we might stay sinners sinning and just no longer be charged
with sin. That is the worlds view of getting away free while being evil. And it just leads
to judgement. Only blind people would fall for this. It is like saying I am cured of heroin
addiction while injecting it into ones arm.

6 No one who lives in him keeps on sinning. No one who continues to sin has either seen him or known him.
7 Dear children, do not let anyone lead you astray. He who does what is right is righteous, just as he is righteous.
8 He who does what is sinful is of the devil, because the devil has been sinning from the beginning. The reason the Son of God appeared was to destroy the devil's work.
1 John 3

And why would we desire sin if we abide in the Son of God?

In Christ we have 3 righteousnesses
Faith, Heart, Action
Our faith is counted as righteousness before God
Our faith purifies our hearts as we open up to Jesus and let the Holy Spirit in.
Love is set free, life becomes real, hatred and bitterness go, and we rejoice in
Him.
Our actions reflect this love and joy, the change in our hearts to bring glory
to His name and serve others. Amen.

Meaning how He paid the penalty for sinners by dying on the cross?

That’s fine...if you properly define “believers”.

In Christ we only have one righteousness whcih matters.

The righteousness of Christ, Imputed to us, just as it was imputed to abraham, This is imputed for the same reason Abraham received it, By faith in God

This is called positional or imputed righteousness (we are seen as righteous through Christ)

Our righteousness are as filthy rags, as {aul says to titus, it is not by our righteus deeds we are saved but by Gods mercy

Please do not listen to these self righteous people who think they can live a way which allows God to let them in heaven based on how good they are. They are as deceived as the jews who crucified christ were .

How do we know we are following the real Jesus and not another Jesus? Paul gave us warning of being decieved into following another Jesus:

2 Corinthians 11: KJV
2 "For I am jealous over you with godly jealousy: for I have espoused you to one husband, that I may present you as a chaste virgin to Christ. {3} But I fear, lest by any means, as the serpent beguiled Eve through his subtilty, so your minds should be corrupted from the simplicity that is in Christ. {4} For if he that cometh preacheth another Jesus, whom we have not preached, or if ye receive another spirit, which ye have not received, or another gospel, which ye have not accepted, ye might well bear with him."

We know we are followers of the real Jesus when we believe His Words.. His teachings..

John 6: KJV
63 "It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life."

This is a proposal that is one step too far.
Christ died and rose so that we might walk like Him, that who He is might become our
heart and our walk.

We are always in Christ, so all we are is Him and His word in us.
So the step too far is that we can stand alone in our deeds or our work.
Our deeds are His deeds, our work is His work.

So the step too far is to deny victory by saying walking the path is self righteousness and
not the fruit of the cross, the way of humbleness and meekness. The badge that we are
transformed is our hearts and our walk. Those who rebel and continue in sin, declare there
hearts are dark, their path is not Christs and they do not know Him.

Yes Jesus suffered the death penalty that is upon all humans who have sinned... His death paid the penalty for all who believe Him and trust that His death pays the penalty for their sins..

Do you hold that even though Jesus cleanses and purifies us we are still bound
to sin?

You are correct there. The instructions for establishing a doctrine is as follows, stated in both the OT and NT

Deuteronomy 19:15 One witness shall not rise up against a man for any iniquity, or for any sin, in any sin that he sinneth: at the mouth of two witnesses, or at the mouth of three witnesses, shall the matter be established.

2 Corinthians 13:1: This is the third time I am coming to you. In the mouth of two or three witnesses shall every word be established.

Would you change your mind if you realized there are a few other verses that establish the same doctrine that believers are not supposed to be conscious of sins?

Hebrews 10:2, 2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.

Hebrews 10:17 And their sins and iniquities will I remember no more.

This was repeated one more time at Hebrews 8

12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.

Now, if that is not enough, other passages from Paul emphasized that the law is not meant for the believer, thus no sin can be imputed when there is no law, 1 Timothy 1:9, Romans 5:13, Romans 6:4, Romans 4:8.

Now that you have realized these passages exist, is it easier for you to understand?

So according to you, what is the proper definition of "believers"?

The word used for “believers” is more than just a passive acceptance. If I were to apply it to fitness; Although many believe eating vegetables and getting exercise is a good, those who “believe” are the ones eating the vegetables and getting exercise. Saying Jesus is Lord is not salvation. Making Jesus Lord is.

So you lean towards the view that it is faith + works that lead to salvation?

Salvation is rooted in
Romans 10:8-9 (KJV)
8 But what saith it? The word is nigh thee, even in thy mouth, and in thy heart: that is, the word of faith, which we preach;
9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.

It isn't based on the fine details of how what Jesus did was effective. The simplicity of salvation is based on two elements of faith.
Believe in every word concerning Jesus, in essence His whole being.
Believe down deep (in the heart), not just mentally, that God raised Jesus from the dead.

Paul preached about Jesus, and so did others. They all delivered the Word of God. What is recorded of Jesus in the scriptures is to be believed, not at all doubted. There is no good in cherry picking the parts one likes best. We receive Jesus "as is" the way the apostles did, or we have no part in Him.

Jesus was raised from the dead for our own hope of eternal life. Without that act all Christians would be most miserable creatures. Otherwise each of us would be destined to be dead like an autumn leaf, nonexistent in eternity, and lacking an interest in living now for eternal life through the righteousness of Christ.

One passage should be taken as a pattern for life that solidifies our two major elements of faith, keeping our faith alive and growing. That is
2 Peter 1:1-11 (KJV)
1 Simon Peter, a servant and an apostle of Jesus Christ, to them that have obtained like precious faith with us through the righteousness of God and our Saviour Jesus Christ:
2 Grace and peace be multiplied unto you through the knowledge of God, and of Jesus our Lord,
3 According as his divine power hath given unto us all things that pertain unto life and godliness, through the knowledge of him that hath called us to glory and virtue:
4 Whereby are given unto us exceeding great and precious promises: that by these ye might be partakers of the divine nature, having escaped the corruption that is in the world through lust.
5 And beside this, giving all diligence, add to your faith virtue; and to virtue knowledge;
6 And to knowledge temperance; and to temperance patience; and to patience godliness;
7 And to godliness brotherly kindness; and to brotherly kindness charity.
8 For if these things be in you, and abound, they make you that ye shall neither be barren nor unfruitful in the knowledge of our Lord Jesus Christ.
9 But he that lacketh these things is blind, and cannot see afar off, and hath forgotten that he was purged from his old sins.
10 Wherefore the rather, brethren, give diligence to make your calling and election sure: for if ye do these things, ye shall never fall:
11 For so an entrance shall be ministered unto you abundantly into the everlasting kingdom of our Lord and Saviour Jesus Christ.

Those are not a list of required works unto salvation, but describe what every believer can do to remain in faith, not neglecting faith unto salvation as many do over their years of living in the flesh. I look at this a like establishing a vegetable garden, then maintaining it by watering, weeding, feeding, harvesting appropriately. The more one learns of that process, the better the future harvests. But neglecting the vital parts results in a failing garden suffering from neglect.

The "fruit of the Spirit" is what God is looking for, the true harvest of His garden.
Galatians 5:22-26 (KJV)
22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith,
23 Meekness, temperance: against such there is no law.
24 And they that are Christ's have crucified the flesh with the affections and lusts.
25 If we live in the Spirit, let us also walk in the Spirit.
26 Let us not be desirous of vain glory, provoking one another, envying one another.

What Peter wrote is what promotes those values that Paul verified.

If you plant a peach tree but never return to it to maintain it, you might have a tree, but no fruit worth harvesting. Nice peaches require a maintenance, like watering, pruning excess flowers and inner branches, thinning excess fruit to control the weight-carrying ability of each branch.

The issue is "Do you know Jesus and believe His good news, that He is master (Lord) instead of you owning yourself in self confidence; and since (not "if") God raised Him from the dead, you too follow Jesus from death to eternal life in Christ?"

So believe the New Testament and live it's precepts however you can all the days of your life to live a full and pleasing living sacrifice to God. Be an ambassador for Lord Jesus, king of kings, Lord of lords.

Avoid spreading out Jesus' lordship all the way back to Genesis. Mos people become Christians without an Old Testament knowledge. What matters is Christ in you today, every day.

John 1:14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.

Luke 2:40 And the child grew, and waxed strong in spirit, filled with wisdom: and the grace of God was upon him.

John 1:17 For the law was given by Moses, but grace and truth came by Jesus Christ.

2 Timothy 1:9 Who hath saved us, and called us with an holy calling, not according to our works, but according to his own purpose and grace, which was given us in Christ Jesus before the world began,

The definition of Grace is Jesus Christ. We are saved by grace (Jesus Christ) and not of works so that no man may boast. Being under grace means you are bound under Jesus Christ. In Jesus Christ there is no sin. So if indeed you are in Christ or under "grace" (Jesus Christ) you will repent from sin. He left us His Holy Spirit to be able to do such a thing. And if we are lead by the Spirit we will walk in love and in truth. These have no consequence of the law.

So if you are under Jesus Christ you are no longer under the law. If you walk in the Spirit. Our sins have been imputed to Jesus' blood. But those who belong to Jesus obey His commands and follow Him. Denying themselves. If we remain on the path and endure until the end we have our due reward. The promise of salvation.

John 14:20 At that day ye shall know that I am in my Father, and ye in me, and I in you.
21 He that hath my commandments, and keepeth them, he it is that loveth me: and he that loveth me shall be loved of my Father, and I will love him, and will manifest myself to him.
22 Judas saith unto him, not Iscariot, Lord, how is it that thou wilt manifest thyself unto us, and not unto the world?
23 Jesus answered and said unto him, If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him.
24 He that loveth me not keepeth not my sayings: and the word which ye hear is not mine, but the Father's which sent me.

The gospel is about the good news of the kingdom of God. Jesus paid our debt allowing us to be reconciled to God and have the hope of eternity with Him in the kingdom of God. Jesus is Lord. and we can share in this as heirs with Christ. Through Faith. Through believeing. Through surrending ourselves to Jesus.

James 4:6 But he giveth more grace. Wherefore he saith, God resisteth the proud, but giveth grace unto the humble.
7 Submit yourselves therefore to God. Resist the devil, and he will flee from you.
8 Draw nigh to God, and he will draw nigh to you. Cleanse your hands, ye sinners; and purify your hearts, ye double minded.
9 Be afflicted, and mourn, and weep: let your laughter be turned to mourning, and your joy to heaviness.
10 Humble yourselves in the sight of the Lord, and he shall lift you up.

So your belief is that no one can be sure of their salvation while they are living on this earth?