I usually say I finished my class, and my friend told me he says I'm done my class. Is it proper or not?
Your friend is only partially correct. "I finished my class" is correct if you have recently finished and you're telling your friend that you're now free to do other things. If you want to use "done", then you'd only use it if you have several classes, and you'd say, "I'm done with my classes (for today)".