What to use to stick it on? Hrm... I would imagine double-sided sticky tape should be fine since it will be covered. You'd probably want to seal the background on from the bottom of it as well as the sides though, so the snake doesn't try to get behind it. Not sure if it would, but you never know!
As for sealing up holes, go to the fish section for that, too.

They sell silicone sealant to fix tanks and glue together rocks and such for displays in fish aquariums. Once it cures it's completely safe, though it does smell awfully strong of vinegar while it's curing! I've used it before in repairs, and it's easy enough to work with. Just fill up the hole with it, let sit for several days to thoroughly dry, and it should be fine. Unless someone with more snake knowledge would know a reason it might harm a snake? Can't imagine it would, since it's safe for fish once dry. Would seem to be a better choice than wax, though.
For the matter, you might also use the sealant to secure the background, too. It would be a bit harder to remove later if you wanted to, but you could.