Yes, “covenant” means a relationship. Genesis says that God is committing to an everlasting relationship with humanity. But it would be wrong here to conflate “covenant” with “the Mosaic Law”. If you recall, God also established covenants with Noah and with Abraham which predate the Mosaic Law. So the words can’t be equivalent.
So, for a past period in Israel’s history, God related to one people-group through the Mosaic Law. Now that Jesus has come and fulfilled the Old Covenant, we (both Jews and Gentiles) are to relate to God in the form of a New Covenant (i.e., in Jesus)…
There are multiple OT covenants – Noahic, Abrahamic, Mosaic and Davidic, but the Mosaic Covenant is the one most people think of and it is the most developed, and equating it with Mosaic Law is pretty much a given I think.
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Yes, when Jesus is disputing with the Pharisees he does indeed specifically refer to “The Law of Moses”, and this is what Paul refers to as the “Old Covenant”, the thing that Jesus surpasses. My point is that just because God tells Abraham that his “covenant” is everlasting this doesn’t equate to “Obeying the Law of Moses is the way that humanity will relate to me for all time”.
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“Do this and you will live, don’t and you will die” pretty much summarizes it, but encapsulated in it is also moral law, laws of love – to love God and love your neighbor, with some specific how to’s articulated that have not gone away. That speaks to all time.
Yes, Jesus summarized that all that was important to glean from the Law of Moses was “Love your God and love your neighbour”. And, as Christians, the fundamental difference is that we demonstrate such love as a result of what God has already done for us (through grace), not because ritualistically keeping a law is necessary to earn God’s favour.
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Absolutely. We still need to keep the laws of love though.
(We talked about it not too long ago. ; - )
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Yes, let’s just say that if there is no evidence of love in our M.O., that one has a right to question the vibrancy of our “faith”.
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Exactly, and we are given tools by which we can measure the evidence, and not just incidentally test ourselves as well, as Paul mandates.
One example among several:
Examine yourselves to see whether you are living in the faith. Test yourselves. Do you not realize that Jesus Christ is in you? – unless, indeed, you fail to meet the test!
2 Corinthians 13:5;
If I am routinely getting traffic tickets, I am not passing any vibrancy tests nor being edified by the coercion (to use a non-threatening and impersonal example ; - )!
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Tee Hee. I’m guilty of one or two of those traffic tickets myself! I need to learn to love better!
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I’ve gotten fewer than I deserve. 
(Only one speeding ticket in all my years, in my youth and when my wife-to-be was with me, and we’ve been married over half a century. ; - ) But I have enjoyed driving in say D.C. rush hour when it’s rushing and not stopped bumper to bumper. It can be exhilarating, but I wouldn’t want to have to do it routinely!
I agree, He did keep the law perfectly, but where does scripture say that He did so from birth? Jesus said, “I am the way, the truth and the life”, but what is the way in which we can we follow Him if He was born perfect? Wouldn’t that be an advantage that we, who are not born perfect, have no chance of overcoming?
In Galatians 4:4, it says that Jesus was born under the Law. Doesn’t that suggest that He had to do something in order to satisfy the law? Also, in Romans 8:3 it says that He was sent in the likeness of sinful flesh. Then, in Hebrews 7:26, it says that He was separated from sinners. Doesn’t this imply that at one point He wasn’t separate? Peter 1:4 seems to agree with this when it says that Jesus escaped from the corruption in the world caused by evil desires. I think that this is what Jesus was talking about when He said, in John 16:33, that He has overcome the world. In 1 peter 2, Jesus gives us steps to follow that we might follow in His steps. How can He give us steps that we can follow if He was perfect from birth?
I found this theological commentary of Galatians 4:4 online:
“Jesus was born a Jew, into a human Jewish family in Israel. As such, He was born “under the law.” Jesus was the only human being ever to keep the law perfectly. In doing so, He declared that He had “fulfilled” the law (Matthew 5:17). He satisfied all of its requirements, then died on the cross to pay all of the penalties for the sins of others (Galatians 3:13)”.
I agree with every word of that commentary.
I agree with the first two sentences. The rest get progressively meaningless. Although I agree that’s what Jesus thought.
Of course he didn’t keep the Law from birth. But he kept it perfectly from the time he was conscious of it. But the thing is, Jesus was without sin, according to the scriptures. That is part of orthodox Christian faith, for mainline churches anyway.
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But the covenant God made with Abraham and his descendants is eternal, according to the scriptures. God has not written off his ancient people.
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Hebrews 5:8-9 reads “Although he was a son, he learned obedience through what he suffered. And being made perfect, he became the source of eternal salvation to all who obey him”. Also, Hebrews 2:17 says " Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God, to make propitiation for the sins of the people". Then in Philippians 2:5-8 it reads “Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men. And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross”.
It seems to me that we misunderstand what he did if we say that he was born perfect. I think that the Bible supports the idea that he was fully like us. However, it is also clear that when the Holy Spirit descended upon him, God declared him to be His Son. So, at that point he becomes fully capable of being perfect. Then, in the desert, he proves that he is perfect.
We don’t know much about Jesus before his ministry began, but we do know a little. We know that he had unusual wisdom. We also know that he believed that he was doing his Father’s will. Also, that he wandered off from his parents suggests an independence of mind. These three qualities, all within the range of what is humanly possible, made him uniquely qualified to solve the problem of how to satisfy the law of Moses. So, he was the messiah from birth. However, he did it as a human being who, later in life, was elevated to being the firstborn Son of God.
That does not denote nor imply he was ever disobedient. (Wise people learn from others’ mistakes. That’s as opposed to “Experience is what you get just after you need it.” 
)
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An interesting take related to that is that his death to pay the penalty for sin was for Israel as well, for their failure to fulfill their obligations in the covenant: Experimental Theology: Covenantal Substitutionary Atonement
A quote from that blog:
“ So, God enters history in Jesus to be Israel’s representative, Israel’s Messiah. And as the faithful Israelite Jesus takes up the covenantal burden–both in fulfilling the Torah and in bearing Israel’s punishment in breaking the covenant. In Jesus God does what Israel could not do, stepping in to help Israel fulfill its side of the covenant, which, per ancient Semitic covenantal logic, does include punishments for breaking promises.”
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