Can I Work Part Time And Still Collect Unemployment?

I don't know about all states. In Tennessee, you can work while you are drawing unemployment. However, if you receive the maximum benefits of $278 per week, you can only earn wages up to $64 dollars. Your local unemployment office should be able to tell you how much you can earn and still draw your unemployment.

I live in NJ I can collect unemployment if I work only 20 hours?

It depends on what state you work in, each one has it's own set of rules. The best way to find out is to contact your local unemployment office.