I think your questions are good and they show what false teachers and false doctrines have done to many people. People are taught that obeying in any way is impossible, filthy, and wrong. Some separate Jesus from the old law and separate Paul from Jesus. As if Paul taught their strange doctrine of believe and you can't obey anything, or as the Calvinists teach that we cannot even believe without a special enabling from God. Peter and James rebuke this strange don't obey misunderstanding about Paul, and they call people ignorant, uneducated, and fools. See all of 2 Peter Chapter 3, and especially 2 Peter 3:16, and 17. After Peter calls people uneducated and ignorant, he warns us to obey. James says it is foolish to think we only have to believe. James says faith alone is dead and cannot save anyone. See James 2:14, 17, 19, 22, 24, and 29.
Common sense escapes them and they cannot be reasoned with about their misunderstanding.
The old law was strict and the people had to clean themselves so that God would live among them and call them His people. Some people would only obey out of fear of God; and others obeyed God out of fear and also out of faith. God did not like it that the people would give sin offerings but not really be sorry for their sins. God said that He would make a New Covenant one day and that He would clean the people.
Jesus came to give that New Covenant. Jesus gave the rules and regulations for the New Covenant, and then like the lambs that had their blood shed to clean the people, Jesus was the last Lamb, to clean people of their sins, once and for all.
The Apostles preached and taught Jesus to the Jews, and Gentiles, and then Paul was brought in to the ministry and the Jews didn't trust Paul, because he had Christian Jews, men and women dragged out of their homes and put in prison to be tortured and killed. So Jesus sent Paul far away to the Gentiles.
The Bible never ever tells us that we no longer have to obey God. The 'not of works' is about not working at cleaning ourselves as once was the law. Jesus cleans us now. We still have to obey. We come to God though Jesus and ask God to forgive us through Jesus. We repent of our sins and call on Jesus to help us. Jesus gives us his Holy Spirit to help us.
I can say that I do not agree with you. I have a problem with the following.
You said,
Jesus was not last Lamb
and
The 'not of works' is about not working at cleaning ourselves as once was the law. Jesus cleans us now.
You did correct the first of these.
As for the second I do not know what you are combatting but it makes sense to me to only speak what I know to be true. This is in teaching. Addressing false doctrines is also something a teacher might do. There are different kinds of teachers. But, or, however, being taught the truth is much desired, more so than being taught lies or what lies or the lies are that are out there. A difficulty might be if you have been taught a lie but no one ever explained to you how it was wrong.
Shalom.
Jacob