100 gallon is way too big, especially for a young BP. If nothing else, you're probably going to have to section parts of it off.
And cat's and snakes don't really get along from what I've heard. Keep an eye on your cat and make sure that lid is secure. I would do everything possible to get that cat to stop hanging out up there, it certainly won't make your snake feel relaxed.
Also, you will need your heat source before you get a snake. Under the Tank Heaters are much better than heat lamps because lamps dry the air out.
Your snake needs an air temp in the 80s, with a hot spot of 92-94 and a cool spot in the mid 80s.
I suggest reading the care sheet...