1. That depends on the temp of the room it is in. Maybe... But, probably not. You may need a heat lamp as well. I've done that in tubs and it works fine. A CHE will as well.
2. That will depend on the size of the snake and the room you have to work with. Hardware stores will have closet rod holders like these in different sizes. They come in wood as well but I got plastic so they are easy to clean.
PRIME-LINE N 6568 Closet Pole Sockets, 1-3/8 in., Plastic, White https://www.amazon.com/dp/B007UTSALU...ing=UTF8&psc=1
That would be easy to epoxy or bolt into a plastic tub.... And PVC cage. I actually just bought those to make some perches myself. I have a bamboo thicket in my backyard I'm going to get the perches from.
3. Same as 2.