If properly attached and with a rheostat/dimmer the uth will maintain a correct hot"SPOT" even if the room temp drops into the 50's, a uth has nothing to do with the ambient temps. Yes substrate plays a small part in this. Your snake benefits from the hotspot by making contact and absorbing the heat from the area the uth is making contact with the tank. If the room your snake is being kept in stays between 75 and 80℉ you will be fine.
I would assume that the UTH would be properly attached to the tank. A UTH contributes a little to the ambient temp in the tank(the heat doesn't just stop at the snake) but I agree that it has very little effect on the ambient temps in a glass aquarium. The ambient room temp however, will effect the UTH from my experience, but then again it's been years since I have used a aquariums for my snakes. I would like to see a hotspot in a tank with substrate in 50 degree weather. I also agree that if you have a room temp of 75-80 then you will be fine, I prefer to keep my ambient temps between that.

This depends .... Ball pythons need a light cycle to justify day and night. The OP never specified the type of room the ball python is being kept in. I myself work a late shift so I have black out curtains in my bedroom. It is always dark in my bedroom unless I actually turn my light on, So If I were to keep my snakes in my bedroom they would need to be provided a day/night light cycle. If the OP is keeping the snake in a room with no window this also applies. If light can flow into the room normally as the sun comes up and goes down then this won't be an issue. Ball pythons do not need uv rays or direct sunlight .... Just enough to differentiate the change of day and night.
I am going to have to disagree, ball pythons do not NEED a day/night cycle. If they did everyone would have LEDs in they're rack systems, but it also is not going to hurt if you want to give your snake one. Maybe in the wild it is useful so they know when to hide from predators during the day.