I eat really late at night. Will my cycle cause my body to create acid at ridiculous times?

I don't understand. exactly what you're asking, but if by "my cycle" you mean your menstrual cycle , then definitely NO, it has no effect at all on gastric acid.
Yes. Eating late can be problematic if you are going to sleep after your meals. Eating triggers our stomachs to make acid and this then can lead to acid reflux. Ideally it's better to eat early, especially for the larger meal of the day.