"On Monday" would mean specifically on that day, but "by Monday" would mean it can happen on any day leading up to that day. Homework or a project due by Monday can be turned in on any day before Monday or on Monday. "Up to Monday" isn't really used, it's a strange wording but you could use it in the same sense as "by Monday" if you really wanted to.

Up to Monday means that something will continue to happen until Monday. I don't think many native English speakers would use 'up to Monday', they'd probably say 'until Monday'. On Monday means that something will happen when Monday comes. By Monday means that something will happen before Monday comes.

Yes but I wasn't sure if my guesses were correct. I thought I should ask it from native speakers of English.

Have you tried to work it out?