Part 1
What is the NT definition of "the law?"
If there are two "most important" subjects in the NT, understanding what the law means is one of them because without it there will be no personal awareness/experience of grace (The New Covenant).
In Romans 10:5 and Galatians 3:12, Paul quotes Leviticus 18:5 and defines the law within this phrase: "The man who does these things will live by them." These texts, along with many others, represent the primary principle of the law you were arranged under/subjected to (Chapter 1), which is: Receiving from God depends on you. If you do x, God will do y. This concept forms the foundation of the law for righteousness in the Old Covenant and is universally taught in today's Christian/Catholic church as the New Covenant. (It's also at the heart of karma, reaping what you sow, self-help psychology, and every religion or new age system of thought propagated by sinful human nature around the world.)
Deuteronomy 30:15-20 sums up the law by telling Israel if they choose to keep the law, God will bless them; if they don't, they will be cursed. Translation: Whether you experience blessing or cursing in your life depends on you. I.e., The man who does these things will live by them...the law for righteousness.
Therefore, according to the law for righteousness, receiving from God depends on you.