starting with question 1 here
we also, as Christians, are in covenant with our Creator. In case you didn't know, there are 5 main covenants in the Bible and it helps to understand how covenants worked in history and to understand that they are binding. We are in what is called the New Covenant, enacted by Jesus when He died in our place, thereby fulfilling the judgement of God against all sin...death. We know He was raised to life because He was without sin and God accepted this atonement on our behalf...in fact it was God's plan all along. This covenant is binding.
The covenants God made with the Israelites were all broken but not by God. Therefore, as God keeps covenant He promises to do for them what they could not do for themselves. He, God, will do for them what they could not do for themselves...keep covenant. Moving across time here, we enter the New Covenant through the blood of Christ. You know that thousands of animals were sacrificed but their blood never actually removed sin as does the blood of Christ. That, is why the Bible describes these sacrifices, and the law(s) as a SHADOW of what was to come...see Colossians 2
Way back in Genesis, God promised salvation and His plan was always to send Jesus to fulfill that promise and create an everlasting covenant with all who are His...both Jew and Gentile alike.
Hebrews helps us to understand more about this covenant through Jesus:
11Now if perfection could have been attained through the Levitical priesthood (for on this basis the people received the law), why was there still need for another priest to appear—one in the order of Melchizedek and not in the order of Aaron?
12For when the priesthood is changed, the law must be changed as well.
13He of whom these things are said belonged to a different tribe, from which no one has ever served at the altar.
14For it is clear that our Lord descended from Judah, a tribe as to which Moses said nothing about priests.
15And this point is even more clear if another priest like Melchizedek appears,
16one who has become a priest not by a law of succession, but by the power of an indestructible life.
17For it is testified:
“You are a priest forever
in the order of Melchizedek.”
18So the former commandment is set aside because it was weak and useless
19(for the law made nothing perfect), and a better hope is introduced, by which we draw near to God.
20And none of this happened without an oath. For others became priests without an oath,
21but Jesus became a priest with an oath by the One who said to Him:
“The Lord has sworn and will not change His mind:
‘You are a priest forever.’ ”
22Because of this oath, Jesus has become the guarantee of a better covenant. Hebrews 7
So, has God fulfilled the words in Jeremiah you quote? Absolutely to all who believe. We are the Israel of God (I believe that God is not done with Israel as some believe but that is another issue for another time) and He has sent the Holy Spirit to bring to our minds all we have learned and to dwell in our 'hearts'.
We have had our sins forgiven and the Holy Spirit indwells believers in Christ to enable us to walk after Christ...to walk in the Spirit, scripture states, and to be able to resist temptation to sin and so on. So what people could not do, as our sin nature overrides every time, God Himself did in giving us the Holy Spirit. We are 'born again' and the law given to Moses, that no one can keep, has been fulfilled by Christ and God's degree that all who sin shall die, is not hanging over our heads.
When we sin, our High Priest (Hebrews) declares us innocent before God because of His blood shed on our behalf. No one should say they are without sin or that they never sin. John says this:
My dear children, I write this to you so that you will not sin. But if anybody does sin, we have an advocate with the Father—Jesus Christ, the Righteous One. 2 He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world.
I John
The 10 commandments reveal a way to live in the love of God but no one can keep them. If you break one you break them all. Jesus said to His disciples:
34A new commandment I give you: Love one another. As I have loved you, so you also must love one another.
35By this everyone will know that you are My disciples, if you love one another.”
It is about love...God is love...all He does is love, including what we do not understand or do not want to accept
All of the above is a very condensed explanation. It's still pretty long though. It's alot to grasp and people spend years studying. Even as I wrote it, I see again the plan of God and how perfect it is. Please understand that there is far more to grasp and understanding comes through the Spirit of God