First. Does your intelligence effect what job you can get and how much promotions?

And second can you quit your job?

Yes, they do.

I think you can quit too. I'm almost 100% sure.

Anything else effects it besides promotions?

Intelligence also effects the creation and use of scrolls at the Secluded Shrine for battling. I'm sure you could see the Battle forums for specific details. :)

Sorry i asked wrong. I meant anything else that effects promotions and jobs that you can get besides inteligence

Its just intelligence but even then its still random.