In response to the title of this thread only, if one need ask which laws are written on the heart, it is a good idea to read the law in the Old Testament, but first know what Jesus teaches about the law.
The law, engraved on stone leaves no room for mercy, however when we have it written in our inward parts, on our hearts, and know our Lord loves mercy, we gladly show mercy where a law may call for severity.
All too many of our brethren assume that the law is abolished, but when reading, studying the law, we can discern by the Holy Spirit which laws should not be observed. We know this also by the Example of Jesus Christ. Some foolish people, who claim to have studied and believe all of the Word, discount the wisdom of the law..
Does not the Holy Spirit residing in you tell you that if you come across lost property of an enemy, you should return it to him? And if you are aware of the parable of the Sower and the seed and the earth, then you know that the law to not sow two kinds of seed in the same field is very wise indeed. The Sower is the Lord, Jesus Christ, the seed is His Teaching, and the field or earth is mankind. It would be wrong to introduce another gospel, not that there is one, instead of the pure truth from our blessed Savior.
The Holy Spirit, and mercy will show all how to obey the law. When your disceern the laws, you will see that your new nature already has you observing them in the spirit, so do not be afraid to know the law, as long as your first faith is in Jesus Christ and the mercy and grace He has given us all.