You have hit on a great subject. But first let me answer directly in case you discard the rest. The Law is ONLY given to Israel. It only applies to Israel and anyone who lived within their borders. So without any explanation, this teaching applies to Israel.
BUT ....
Do you know the difference between INHERITING LIFE and HAVING LIFE? There are two sets of scriptures. One set of scriptures show how to HAVE (intrinsically) Life, and they are always connected to FAITH, e.g. John 3:15; "That whosoever believeth in him should not perish, but have eternal life." And there are another set of scriptures that show how to ENTER or INHERIT Life as a REWARD or POSSESSION, and they are always connected to WORKS, e.g. Mark 10:17; "And when he was gone forth into the way, there came one running, and kneeled to him, and asked him, Good Master, what shall I do that I may inherit eternal life?"
The explanation of this difference is seen in Mark 9:43-48;
43 "And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched:
44 Where their worm dieth not, and the fire is not quenched.
45 And if thy foot offend thee, cut it off: it is better for thee to enter halt into life, than having two feet to be cast into hell, into the fire that never shall be quenched:
46 Where their worm dieth not, and the fire is not quenched.
47 And if thine eye offend thee, pluck it out: it is better for thee to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire:
48 Where their worm dieth not, and the fire is not quenched."
It is at once clear that our Lord uses "entering LIFE" (vs.43, 45) INTERCHANGEABLY with "entering the Kingdom of God" (v.47). The Kingdom of God is that Kingdom predcited in Daniel Chapter 2 when God crushes Gentile rule on earth and has His will done on earth, as our Lord Jesus prayed in Matthew 6:10, "Thy kingdom come. Thy will be done in earth, as it is in heaven." It is for this Kingdom that we are to be born again and Baptized (Jn.3:3-5). So faith is for rebirth were we HAVE Eternal Life (Jn.3:15-16), and when those who HAVE this LIFE, become co-kings with Christ, it is ENTERING a Kingdom of LIFE. The mark of this present earthly government is that the Gentiles, who are "dead in their sins", rule. The mark of the coming Kingdom of God on this earth is that it is a RULE by men who HAVE Eternal Life. Their reign will be permeated by the divine nature.
So, to HAVE LIFE one needs FAITH, but to ENTER the (Kingdom of) LIFE one needs righteous WORKS. In the scripture above from Mark, one is cut ut of the Kingdom because of OFFENSE - a work. This is clearly stated in Matthew 7:21-23. Only those who DO the will of God may enter the Kingdom. So when the Israelite in Luke 10 asked about entering, or inheriting LIFE, He was told to do the will of God - which for the Israelite - THE LAW. But once Israel, as a nation, had rejected Christ, He formally rips the Kingdom from them as a nation (Matt.21:43). Christ then raises up a "New Man" for this job of reigning. The rules then change. A New Birth is required to make one "partaker of the divine nature" (2nd Pet.1:4), and the Law as a means to ENTER LIFE (or the Kingdom), is nailed to the cross. From then on, INHERITING the Kingdom is achieved by "being led" by the indwelling Spirit of God (Rom.8:14, 17).
The thing to remember is that one is SAVED by FAITH. The process of atonement, rebirth, justification and sanctification is by what we BELIEVE. But we are saved FOR the Kingdom. That is the goal of salvation. But the Kingdom is only to be had by proving, by your OBEDIENCE to God. This is achieved by WORKS. You HAVE LIFE by FAITH, and you ENTER, or INHERIT LIFE (the Kingdom) by WORKS. One is an intrinsic CONDITION of being a son of God. The other is a REWARD for OBEDIENCE.