If I have had mouth ulcers in the past, is there a higher chance of them coming back?

Yup. That herpes simplex is a shiftless, no good sidewinder that hides way, way back along the nerve path. Never heard of complete & total eradication. So have Acyclovir at the ready. Keep it scared, real scared.
Depends. That depends on the source of an ulcer. Oral herpes can be provoked and recur.