This is a very complicated topic. I will try being as clear as possible but if you still do not understand please leave a comment by clicking here or commenting down bellow. I would have given this response.
First, we need to understanding of the purpose of the law. The law is God's Holy standard. The law was given to show how bad, sinful and how we hate God and his ways (Romans 5:10). The Ten Commandments show us that we cannot meet God's standard. Take an example out of your life. One of the commandments says that you shouldn't lie. How many times have you lied? How many times have you disrespected your parents? How many times have you put things before God? That offends a Holy and perfect God. God is offended every time you sin. It shows how much we hate God. To make matters worse when we look to Leviticus (Leviticus 19) we see that there's a higher standard that we will be able to keep.
That we shouldn't reap grapes from the outer parts of vineyards, do not wear clothes woven from two different fabric. That if you have a garden you are only supposed to have one plant. Don't have tattoos. Only eat well done meat. Do not eat pork. Do not work from Friday 6 o clock 'til Saturday 6 o clock (the Sabbath). Those are the standards given to the Israelites to set them apart. And these are just a few of them. There are many more.
All of that to show that we ALL are bad people, haters of God and there is nothing we can offer God. That our own righteousness (trying to keep the law and being good) is like a bloody tampon before God (1 Cor 4:13). For all have sinned and fell short of the glory of God. (Romans 3:23) There is none righteous (righteous meaning never committed a single sin) no not one! (Romans 3:10)
Paul says God has done this so that no man can boast in his action. But so that we should point to God is the only one who is able to keep his own standards so in the end He can be glorified! Christ came and forgave us for all those laws we continue to break because we CANNOT keep them.
Now let's answer the questions since we have the back story of the purpose of the law.
Christ did not come to abolish the law but to fulfill it
We shouldn't live in sin.
Grace does not abolish the law. It does the opposite. It shows the law has been fulfilled. Christ was punished on the cross on our behalf although we hated God to fulfil the law. Once we are Christians, we want to keep the law out of gratitude. It is impossible to be saved and not have actions but it is possible to have actions and not be saved.
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