The UTH is indeed fastened by aluminum tape, this tape is more flame resistant than others. The probe should be taped to the UTH (it's the silver bullet type thing in the first pic of the thread you linked). As long as there's a gap between the ground and UTH so air can escape (and temps are at the reccomended heat for BPs) then there isn't a fire hazard. Constant contact can build up heat and cause warping plastic and at worst of times melt it. As for the luggage straps, I'm not 100% on them since I've personally never used them. I use binder clips to pin the lid myself. The tub can be set on top of any shelf really.

Have fun with your new snake! Feel free to ask me or anyone else on the forum any other questions.