That is one of the FEW exceptions IMO. However, for the most part at 18 you should be okay to not have to use the bathroom for 50 minutes. You use the bathroom before class.
Anyway to the OP, those are not strict at all. 4 pages is not a lot of writing, and if you need help go to the writing center or tutoring center.
Why should the professor accept your being late? It’s disrespectful.
I think you are severely over reacting. HIs rules are plenty fair