The words "works of the Law" mentioned in the New Testament is in reference to the works of the Law of Moses or the Old Covenant Law .
For the words "works of the Law" appears 5 times in Scripture.
https://www.blueletterbible.org/search/search.cfm?Criteria=works+of+the+law&t=KJV#s=s_primary_0_1
And it is clearly in reference to the Law of Moses.
Romans 9 is about Israel, so there is no point showing you that the words "works of the Law" is clearly in reference to the Law that they kept.
The other occurence of the words "works of the Law" is mentioned in Galatians and also is in reference to the Law of Moses. It is evident by just reading the chapter. But here is a bread crumb or clue that makes it obvious.
"why compellest thou the Gentiles to live as do the Jews?" (Galatians 2:14).
The other 3 occurrences of the words: "works of the Law" is in Galatians 3. Again, it is obvious this talking about the Law of Moses because of many bread crumbs or clues contained therein. For one, it says the Law was added because of transgressions (Galatians 3:19). Second, it says the Law is a school master that brings us unto Christ (Galatians 3:24).
"Works of law" is certainly related to the law of Moses, but only so far it is in regard to man-made traditions for how to keep the law of Moses, so it is not something directly commanded by God. It was common for certain groups to say that you needed to obey the law according to their traditions in order to be saved. For instance, with the discovery of the Dead Sea Scrolls Qumran text 4QMMT, we have:
Now, we have written to you some of the
works of the Law, those which we determined would be beneficial for you and your people, because we have seen [that] you possess insight and knowledge of the Law. Understand all these things and beseech Him to set your counsel straight and so keep you away from evil thoughts and the counsel of Belial. Then you shall rejoice at the end time when you find the essence of our words to be true. And
it will be reckoned to you as righteousness, in that you have done what is right and good before Him, to your own benefit and to that of Israel. (p. 364, Dead Sea Scrolls: A New Translation)
In other words they are saying that if you keep our traditions, then you will be saved. Much of the discussion about the law in the NT is about the way that God should be obeyed, not about whether God should be obeyed. Compelling Gentiles to live as Jews is another example that is talking about Jewish traditions rather than God's law. The Jewish tradition in question is the one that forbade Jews from meeting with or associating with Gentiles, which Peter mentioned in Acts 10:28, which is why he moved to go eat with the circumcision group. This is the same group in Acts 15:1 that wanted to require Gentiles to keep the law according to the customs of Moses in order to be saved, so they're saying the same type of thing. By moving to eat with them, Peter's actions were saying to the Gentiles that they weren't actually saved and that they needed to go along with what the circumcision group was saying and follow their traditions in order to be saved, which why Paul proceeded to emphasize that we are justified by faith in the next verse.
While I agree for the most part in the 6 points you brought up. I do not agree that we are to obey ceremonial laws or judicial laws in the Law of Moses because Scripture says Christ nailed to the cross those ordinances that were against us. The eternal moral law has been carried over into the New Covenant (Obviously). However, while Jesus did keep the Old Law perfectly, He was also making changes to the Law, too. For Jesus said to turn the other cheek instead of an eye for an eye. Jesus did not condemn the woman caught in the act of adultery. When Jesus died upon the cross, the temple veil was torn. Meaning, the Law that required the animal sacrifices was no longer binding or acceptable. Jesus is now our perfect sacrifice. The priesthood order of Aaron has been disolved or fulfilled in Christ. Jesus is now our Heavenly High Priest (of a new priesthood order). We go to Christ as a mediator and not a physical priest. There are no more Levites. Also, after Christ's death, Peter had a vision from God that he could now eat unclean animals. This a direct violation of OT Law. In fact, Scripture itself states the Law has changed (Hebrews 7:12). Which makes sense because we are under a different Covenant. Jesus said, no man puts new wine into old wine skins.
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What was nailed to crosses was the crimes that the person had committed, not the laws themselves. In other words, they didn't have to legislate new laws every time someone was crucified. This fits perfectly with Messiah being our kinsman redeemer who took the penalty for our sins and set us free from our slavery to sin, but does not fit at all with being set free from a set of holy, righteous, and good instructions. God has no reason to set us free from that, we have no need to be set free of that, nor should we even want to be set free from what is holy, righteous, and good. Rather, the law was meant to be received as a divine privilege and delight, as the Psalmist understood (Psalms 1:1-2, Psalms 119), and as Paul understood Romans 7:22). Sin is the transgression of the law (1 John 3:4), so we have been set free from transgressing the law in order to be free to not transgress the law, not to be free to sin and disregard the law.
Morality is about what we ought to do and we ought to obey God, so all of God's laws are inherently moral laws. Furthermore, the Bible makes no distinctions between moral, civil, and ceremonial laws, but rather the violation of any of God's laws is a sin and immoral. It can be useful to us to fit God's law into different categories, but I see no justification for artificially imposing those categories into the text rather than letting the text speak for itself. The New Covenant involves God's law being written on our hearts (Jeremiah 31:33), so all of God's laws are carried over, with the change only in regard to those laws concerning the Levitical priesthood.
Jesus didn't actually teach anything new, but rather he taught how the law should be fully and correctly understood and obeyed. The woman caught in adultery is another example of how Jesus followed the law rather than changed it. There was no man who was also accused of adultery (Leviticus 20:10), the woman did not confess to her crime, there were no witnesses (Numbers 35:30, Deuteronomy 17:6, Deuteronomy 19:15), and there was no judge to pronounce a sentence (Deuteronomy 19:17-21), so if Jesus had stoned her, then he would have been acting in violation of the due process of the law. Their goal was not to seek justice, but to try to trick Jesus into either speaking against obeying God's law or Roman law.
http://www.ecclesia.org/truth/new.html
There are two curtains that lead to the Holy of Holies, so one curtain being torn in problematic for that interpretation. Furthermore, Paul continue to offer sacrifices, which included sin sacrifices (Acts 18:18, 21:23-24) in accordance with the law (Numbers 6). There will also be sin sacrifices during the Millennium (Ezekiel 44-46). The blood of goats and bulls never took away sin, so they could not be made obsolete by one that did.
In Peter's vision, all kinds of animals were let down in the sheet, so why didn't he obey God's command by simply killing and eating one of the clean animals, as the Torah permits? Why did he object? The answer is that the Pharisees had a man-made ritual purity law that said that if something clean came into contact with something unclean, then it became defiled/impure/common (See
Mark 7:3-4). All of the animals were bundled together, so all of the clean animals were in contact with unclean animals and had become common. Thus all the animals in his vision were either common or unclean and by refusing to eat one of the clean animals that had become common, Peter was disobeying God to obey man. Note that God did not rebuke him by saying not to call unclean what he had made clean, but rather God rebuked him for referring to clean animals as common. So Peter's vision was about correcting a man-made ritual purity law, which Peter interpreted as including the man-made laws about Gentiles (Acts 10:28), and had absolutely nothing to do with God's dietary laws. Peter gave the interpretation of his vision three times and not once did he say anything about dietary laws.
Luke 5:39 says that the old is better, so there are problems with interpreting that Jesus was talking about covenants. To describe Jesus as being incompatible with Judaism is both bad theology and bad history. Rather, the context Jesus was selecting his disciples and was being criticized for his selection because of their behavior. Jesus responded with a double parable that borrowed from Jewish tradition found in Pirkei Avot 4:20. When we use the same symbolism, we see that the old and new garment/wineskins are previous educated/uneducated students, the patch is teaching, and the old/new wine is old/new is previous/new teaching. If you try to teach a lesson meant for a new student to an already educated student, then you will fail to teach the new student and the already educated student will reject it. In response to their criticism about his choice of disciples Jesus essentially replied that you can't teach and old dog new tricks.
