So instead of the 10 Commandants, you have the 7.
Where is no lying or cheating?
I'm afraid to ask what illicit intercourse is.
Lies / Cheating - the basis of the "theft" category is honesty / dishonesty. Also, what is stolen may not be an object. For instance, you can steal a persons good name / reputation by gossiping about them. However, lying to protect a life is, of course, a wonderful thing.
To answer your questions regarding the 10 commandments and illicit intercourse, I have to explain something. In the Bible, what is commanded to Jewish people is not necessarily instructed to Gentiles ( non-Jews, Noahides). There is a big difference.
When you read the Bible passage that lists the 10 Commandments, if you read the surrounding text you can see that they were given to Israel (people / nation) and not to Gentiles. Even in the Christian New Testament texts this can be seen. Gentiles are not obligated to follow all the rules that Jewish people must follow, according to the Bible. That includes observing the Sabbath.
The Noahide category of illicit intercourse includes prohibitions against rape, sex with children, sex with animals, and sex with close relatives (incest). If you are married, you can only have sex with your spouse. If you are not married, you cannot have sex with someone else's spouse.
As most people know, the Bible is not politically correct. But Noahides attempt to live their lives according to instructions in the Bible because we believe them to be given by God. So, a man having sex with a man is considered illicit intercourse in Noahide "law".
Marriage: Again, there is a biblical distinction between Gentiles and Jews. Adam, Eve, Noah, and Abraham all lived before there was an "Israel" / Jewish people. So in their time, everyone was Gentile. When a man began to live with a woman (& have sex with her), they were called husband and wife. If one of them had sex with someone other than their spouse, it was called adultery - illicit intercourse. Later, when Israel came into existance along with commandments that applied only to them, nothing changed for the rest of humanity. They still had the same, original, Noahide laws.
So, when Christians say that premarital sex is prohibited, they are correct regarding Jewish people but not for Gentiles.
Of course, there is a lot more to all this, so feel free to keep the discussion going.