I think that it's better start with the big picture of God's plan.
God is to build a Heaven (an eternity) where He can live with angels and humans forever. In this heavenly land all three parties will be highly satisfactory (no one gets hurt). God is completely sin-compatible. To a certain extent, it means God can be harmed, not in a physical sense though. God can be harmed when His creatures sin. Actually He can be harmed more in another way. That's why He never left His real name to humans, while Jesus will have a new name after the Final Judgment.
So to the first party, who is God, no sin is allowed in Heaven. God either pick those not to sin with Him at will, or designate an open system to qualify them lawfully and legitimately. Law does the job, at the same time Law means, "if you can pass the Final Judgment of Law, God will bear with you in the eternal realm forever." That's the promise of Law.
Now comes the definition of free will. Free will, in terms of Law, means one (angel and human alike) is given the ability to choose to harm God by sinning against Him. All left follows mathematical laws to work (i.e., statistics and probabilities to be specific). By the degree of free will granted, 2/3 angels and 1/3 (less than) humans shall be able to pass the Judgment of Law. This is rather a mathematical Normal Distribution of human and angelic beings. By the formula with a single factor which is free will, the mathematical Expected Outcome points to a narrow gate for humans. At the same time, mathematically there's always a nearly zero probability that there's a distribution shift that "all men are saved" (as a wish). "God wishes all saved" actually represents an extreme mathematical outcome. It's more or less analogue to throwing a coin infinitive number of times while expecting an all head outcome (no matter sheer it is, such a probability exists mathematically).
Besides the factor of free will, another critical factor jams in. Angels are created with high ability and high intelligence (the bad ones can be referred to as the "crafty snake"). It is so because the very existence of the angels is to participate in God's creation tasks. Comparatively, humans are made to be with low ability and low intelligence. The 1/3 bad angels (crafty snakes) can cast an influence to the low intelligence humans (Snake to Adam and Eve). When adding this factor into the formula, humans savable drops to an absolute zero. Just as said, no one (human) is righteous, not even one. As a result, Law protects God from being harmed by the hopelessly meaningless human sins. Law demands a total destruction of humans on earth with the Noah's flood, that is.
Then Jesus' crucifixion offsets the Judgment of Law. The 1/3 humans will be saved through an alternative Judgment of Covenant, instead of the original Judgment of Law (which only angels can pass).
The problem is, how to demonstrate the above to humans on earth? Effectively only angels know Law (of the Judgment of Law). Humans on earth has no way to understand what God's Law could mean, at a more explicit level. God went through His chosen people Israel to demonstrate what God's Law could mean. Mosaic Law is actually under the Mosaic Covenant but for God to demonstrate what His Law could mean. Theologically, the Mosaic Covenant is only with a scope covering the Jews (as signified by circumcision of the male Jews). To the Jews then, Mosaic Law can be called as "God's Law" (as a matter of perspectives). It's God's Law granted to the Jews by means of Moses, serving the purpose of demonstrating what God's Law could mean such that later humans can understand what God's Grace is (wihtout a primitive understanding of Law, no one can tell what Grace could be).
Humans are granted various covenants, in the different period of time covering different scopes of humans. However, these covenants have something in common, you may use the term "commandments" to describe this common part between covenants. In the Mosaic Covenant, commandments are enforced as Law. However in the New Covenant, the common ones are referred to as "Christ Teaching" or "Jesus' commands". This means they are no longer enforced as Law. The nature of Law may sentence you to death when you only violate it only once. When commandments are no longer enforced as Law, you have the chance to repent. Repentence only belongs to humans covenantally but not angels, thanks to Jesus Christ. The New Covenant covers all mankind as its scope of humans, gentiles and Jews alike.
There are two perspectives one can used to describe the nature of Law (with its corresponding Judgment). From the legal and lawful point of view, Law will never be obsolete as all sort of Law and covenants (with their human scopes) will be reserved for the Final Judgment (either of Law for angels or of Covenant for humans). Yet from the perspective of the judgment effect, to humans Law can be deemed "obsolete" when we are talking about humans are no longer subject to the Judgment of Law, with Jesus we are disconnected from the Judgment of Law and are subject to the Judgment of Covenant.
Why is human faith important? The high intelligence can understand most of God's creations, as they are born to participate in the creation jobs. The low intelligence humans can hardly understand God's creations in full (the snake in Eden tells otherwise though). Humans need both faith and obedience in order to live in Heaven where no one gets hurt, including God Himself. Another fold of meaning of human faith is that, it signifies how one is correctable while we all sinned. Human faith and obedience signify that one is correctable (after sinned on earth) in Heaven and will be holy to see God (without harming Him). That is, with faith and obedience to the qualified level (as judged by a Covenant one belongs to), God promises through Law that He will bear with in eternity no matter what. It is so because the saved are capable of faith and obedience and are correctable in the future dwelling realm of our Holy God.