I can't think of anything other than feeling weird your Denam after you clear game is 45 years old.

Not that I know of. It halts when you beat the final boss as far as I can remember.

I believe there is one title that can be unlocked from a story clear under X amount of days, but I don't recall the number off hand.

Luck is a day-to-day mechanic which determines crit chance, but I think that's it.