Are you using a glass tank to house the snake or a plastic sweater box(rubbermaid, iris, sterilite, etc)? Sorry, I got confused when you said "clear tupperware container". Is that going to be the humid hide or the actual enclosure for the snake?

If you need to mist the enclosure, try misting the sides instead of the bedding.

Yes, any vet tech should be able to tell you what parasites(if any) that the snake has. I say "should" lightly... Not every tech(or vet for that matter) can tell what different kinds of parasites are, let alone what species they can inhabit. Weirdos But yes, the one you take your cat too should be able to do a fecal for you. I would just take the fecal sample in there, and ask them if they wouldn't mind doing one. If they have to see the animal first, you can either take the snake to the vet along with the feces, and just have a general exam done as well as the fecal, or you can find another vet who will do a fecal without seeing the animal.

Hope that helped with a few of your questions