Heb. 10:16 and Jer. 31:33 say: I will put/write my laws on their hearts and in their minds. Has that already happened or is it to come in the future?
The Ten Commandments are part of the Law given to Israel, and the Bible teaches that anyone who has placed their faith in Jesus Christ is no longer under law but under grace.
Regarding the law written on our hearts, the Bible teaches that when a person enters into the New Covenant by faith, we receive the Holy Spirit Who writes the law on our hearts. The law written on our hearts is not the Law of Moses but rather is an infinitely greater law.
The law given to Moses consisted of 613 decrees, but the Law of Christ is infinite in scope. For example, Jesus said that lusting was equal to adultery in God’s eyes, and therefore lusting is a sin, however the Law of Moses says nothing about lusting. Therefore, the Law of Moses is not equal to the full law of God.
When we come to faith we receive the complete law of God written on our hearts so that we may know what righteousness requires under all circumstances. The law written on our heart is called the Royal Law or the Law of Liberty or the Law of Christ. We are called to live by the Spirit who guides us into righteousness based on the law written on our hearts, not according to the law of Moses. So we do not obey the law of Christ by following the law of Moses, since these things are different and not equivalent.
For a complete discussion of these matters, we highly encourage you to listen to our entire Romans Bible study.