New Ball Python Owner...Any Advice?

[Slugger04]

WARNING: THIS POST IS REALLY LONG

Hi,

I'm a new BP owner as of yesterday (I'm also new to this forum, so I apologize if I there some norms here that I don't know yet). Her name is Piper, I don't know her age, but she is about 3.5 feet long and, according to the previous owner, about 1700g. I got her from another student at my university who is graduating and needed to sell her before he leaves, but today I am starting to think that he may not have been taking great care of her. Like I said I'm really new to owning a snake and I have some questions/concerns about her behavior that I was hoping someone here could help me answer. I really want to make sure that she is happy and healthy in her new home.

TEMP
So when I bought her she came with with a tank, water bowl, UTH, hide, etc. and everything in it seemed totally fine to me. She liked to stay curled up in her hide which I figured was normal. I was concerned about the temperature though; despite the UTH being plugged in and turned on, the tank thermometer was telling me that the tank was at about 70 degrees on the "hot" side even thought the thermometer on the UTH said 95. Today I discovered that the UTH wasn't working at all which told me that the tank thermometer was correct and the poor thing was freezing cold all night! So I freaked out and went to buy a heat lamp and another thermometer. Now I've got the UTH working and the lamp on which brought the hot side to 86 and the cool side is at 75. The weird thing is, now that I've got the temp up in the hot side, she seems to want to spend all of her time on the cool side. To test this I turned the lamp and UTH off and she went back to the hot side. I turned it back on and she went back to the cool side. Any Idea what's going on?

HAPPINESS
I figured her not wanting to be handled was a combination of a) being in a new home and b) just being a ball python. When I got home today, though, I started to realize that her cage (which I got from the guy yesterday) was actually really disgusting. Like I realized there was poop near the water bowl and some shed under her hide from god knows how long ago, and the humidity was at 90% so the substrate was totally soiled. The second I noticed this I cleaned and disinfected the heck out of the whole tank and replaced the substrate. Now she seems to be more active but she doesn't seem to like it in there as much, like she keeps sniffing around the edges of the tank like she wants out and tries to hide on the cool side. Do you think she is just getting used to being in a clean cage or is she unhappy? Humidity is at 55% now and temp gradient is 75-86.

Also she really doesn't seem to want to be handled by me. I don't know her very well yet, so maybe that's just how she is, but I think it could be because her last owner hadn't been taking care of her. How could I make her more comfortable with me?

FOOD
According to the previous owner, Piper hasn't eaten in about 4 months, which I know is normal for BPs, especially for this time of year. He said that he stopped trying to feed her every single week after two months of fasting and that I shouldn't be concerned until June. That seems a little crazy to me. What do you think about that? Also how often should I be attempting to feed her if she is older and apparently on a serious fast? She doesn't seem skinny at all or overweight.

I know that was a lot, I'm just really new and have a ton of stuff to learn. I really appreciate any advice you all might have.