Modern people have a lot of trouble reconciling Old Testament rules vs. New Testament rules because too few ministers understand the differences or even try to explain it. That allows a LOT of unneccessary confusion. It's impossible to totally answer every aspect of the OP's question, that would require volumes of big books, the best we can do here is try to answer fragments of it.
First thing we need to recognise is that God does not change but, from Adam/Eve to today, HIS revelation to man of what He wants our motivation and conduct to be has indeed changed. He loves us and for our salvation He only requires the right heart to be in us. There is no mandatory checklist of perfection for that, meaning we can't possibly "earn", "deserve" or "buy" our salvation, it's a perfect gift from Jesus to imperfect people who trust and love him as Lord.
The OT is mostly a history of the Hebrews who were ruled by things to do or not do to gain God's favor. Didn't work, wasn't expected to work because He knew it's impossible for weak/fallible humans to accomplish anyway.
The "Law of Moses", aka Ten Commandments, are the core of that and we fail even in that simple law. Therefore God, Father, Son and Holy Spirit, devised a way for men to attain spiritual perfection by substituting the perfection of the Son to us through our willing faith/trust in the coming Messiah (the man God Man/Jesus).
So we, the "Church", i.e., the body of Christ consisting of born again believers, Jew and Gentile, from the Day of Pentecost until the coming Rapture of the saints by faith follow a different set of rules based on the original Ten Rules save one.
The concepts of the original ten laws are actually restated in the NT
(all except the "Seventh Day Sabbath") so they apply to our blessings now. The stated rules are to be followed for later heavenly rewards but NOT for salvation so the old Hebrew rules of daily religious practices and temple sacrifice don't apply to us.
If we read scripture for ourselves and basically understand to whom the varied rules apply, and for what purposes, most of the puzzlement fades away. I think.