Welcome to the world of being a ball python parent LOL. It's really not as complicated as it all sounds. First look through our caresheet so you get the basics downpat of the temps and humidity.
To answer some of your questions, temps and humidity should be stable 24/7 all year round for snakes that aren't breeding so get it dialled in and stick with it.
No branches are needed. These are ground dwellers (actually mostly below ground LOL) and they suck at climbing. Instead of branches make sure to provide two tight fitting - no bigger than the snake is coiled up - hides, one for the cool end, one for the warm end.
The water bowl should be easy to clean, not easily tipped and doesn't have to be big enough for your snake to soak in, they rarely soak if they are happy and healthy. I generally put my bowls on the cool end wedged against a corner to help keep them from being tipped (they get tipped anyways, BP's have a sense of humor about a just cleaned home! lol)
Newspaper is fine as a bedding or you can even go with plain white paper towels if you like. Also fine shred aspen is nice if you prefer a more natural look - just avoid pine and cedar as it's not good for your snake.
What sort of enclosure do you have and how big is it? How are you heating it? What are you using to measure temps and humidity?
The biggest thing with a new snake is to let it be. That's hard but it is best for the snake. Give it at least a week to settle in then feed it whatever the breeder was feeding it in the same way (mice, rats or ASF's - live, f/t or p/k). These snakes are creatures of habit so they tend to do what they know. Switching too much up on them when they are still settling in tends to freak them out a bit.
Breathe....you will get it all....breathe....![]()