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Your first answer is incorrect as it is only a partial answer, and does not say how remission is given or if needed:
Here is how you receive remission of sins:
1) Luke 13:3 - I tell you, no! But unless you repent, you too will all perish.
Mark 16:16 - He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Acts 2:38 - Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Spirit.
Matthew 6:15 - But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.
1 John 1:7 - But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
(1:9) If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
Remission of sins are very much needed in order to receive salvation as the Lord says you will perish if you don't have it.
Your answer to number 2 is also wrong as Apostle Paul says multiple times you have to remain in the faith to receive eternal life:
Romans 2:7
To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:
2 Timothy 4:2-8
Preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching. For the time is coming when people will not endure sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions, and will turn away from listening to the truth and wander off into myths. As for you, always be sober-minded, endure suffering, do the work of an evangelist, fulfill your ministry. For I am already being poured out as a drink offering, and the time of my departure has come.
1 Timothy 4:16
Keep a close watch on yourself and on the teaching. Persist in this, for by so doing you will save both yourself and your hearers.
Romans 11:19-22
Then you will say, “Branches were broken off so that I might be grafted in.” That is true. They were broken off because of their unbelief, but you stand fast through faith. So do not become proud, but fear. For if God did not spare the natural branches, neither will he spare you. Note then the kindness and the severity of God: severity toward those who have fallen, but God's kindness to you, provided you continue in his kindness. Otherwise you too will be cut off.
Colossians 1:22-23
In the body of His flesh through death, to present you holy, and blameless, and above reproach in His sight— if indeed you continue in the faith, grounded and steadfast, and are not moved away from the hope of the gospel which you heard, which was preached to every creature under heaven, of which I, Paul, became a minister.
Acts 20:28-31
28 Therefore take heed to yourselves and to all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood.
29 For I know this, that after my departure savage wolves will come in among you, not sparing the flock.
30 Also from among yourselves men will rise up, speaking perverse things, to draw away the disciples after themselves.
31 Therefore watch, and remember that for three years I did not cease to warn everyone night and day with tears.
Here is how you receive remission of sins:
1) Luke 13:3 - I tell you, no! But unless you repent, you too will all perish.
Mark 16:16 - He that believeth and is baptized shall be saved; but he that believeth not shall be damned.
Acts 2:38 - Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Spirit.
Matthew 6:15 - But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.
1 John 1:7 - But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
(1:9) If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
Remission of sins are very much needed in order to receive salvation as the Lord says you will perish if you don't have it.
Your answer to number 2 is also wrong as Apostle Paul says multiple times you have to remain in the faith to receive eternal life:
Romans 2:7
To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:
2 Timothy 4:2-8
Preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching. For the time is coming when people will not endure sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions, and will turn away from listening to the truth and wander off into myths. As for you, always be sober-minded, endure suffering, do the work of an evangelist, fulfill your ministry. For I am already being poured out as a drink offering, and the time of my departure has come.
1 Timothy 4:16
Keep a close watch on yourself and on the teaching. Persist in this, for by so doing you will save both yourself and your hearers.
Romans 11:19-22
Then you will say, “Branches were broken off so that I might be grafted in.” That is true. They were broken off because of their unbelief, but you stand fast through faith. So do not become proud, but fear. For if God did not spare the natural branches, neither will he spare you. Note then the kindness and the severity of God: severity toward those who have fallen, but God's kindness to you, provided you continue in his kindness. Otherwise you too will be cut off.
Colossians 1:22-23
In the body of His flesh through death, to present you holy, and blameless, and above reproach in His sight— if indeed you continue in the faith, grounded and steadfast, and are not moved away from the hope of the gospel which you heard, which was preached to every creature under heaven, of which I, Paul, became a minister.
Acts 20:28-31
28 Therefore take heed to yourselves and to all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood.
29 For I know this, that after my departure savage wolves will come in among you, not sparing the flock.
30 Also from among yourselves men will rise up, speaking perverse things, to draw away the disciples after themselves.
31 Therefore watch, and remember that for three years I did not cease to warn everyone night and day with tears.
God bless Ken.