When can I use "nan" or "a" after a sentence? Like, depi famn nan kite m nan, m pa t ka dòmi byen, or like, pwoteje ou kont jwisè yo ki deyò a? Or, se sa m vlè a? When can I use them and what are the rules?

You will have to know the rules for the definite articles. Here’s a couple of links: 

The definite articles a, an, la, lan, nan

There are some good exercises there especially toward the bottom.  Let me know if that helped after you've gone through it. Thanks

Haitian Creole ↔ English Reference, Look up Haitian Creole and English Words