I know it is a part time job. How much do they get paid? Also can they have a full time job and be a mixologist part time?

Mixologist isn't a part time job, in the "career" sense. It's a skill. But you can get paid by the hour for choosing "moonlight as a mixologist" from the bar menu at a bar or club (the skill level required for this option varies by bar type). You can work as many hours as you want, whenever you want.

I'm not sure what the pay rate is... but I think it varies per club and according to the quality of drinks you make (tip income).

So yes, it is indeed compatible with a full time job.

It's comparable to playing an instrument for tips. You volunteer to man a bar for as long as you like, and you earn money when other Sims order food or drinks. You can leave your post whenever you choose -- the official mixologist will still be hanging around to take over when you're done.