Over.
Normally, You would wear a dress over a corset, but probobly just a regular shirt would work as well.
Yes, you should wear braces (suspenders) anytime you are wearing a tuxedo, weather you're wearing a cummerbund, vest or going with the exposed waist look. You do not wear a belt with a tuxedo, and...
it goes under your sock therefore the sock will help keep it in place better.