1. Assume everything has them. A fully mature mite can travel 30 feet/hr.
2. Live mites hide deep between the scales and are in the substrate and in nooks and crannies within the cage or on cage furniture. For every 1 you see there's 10 or 15 that you don't. You can't spot the eggs and they stick to things.
3. I prefer the nix method. The search function of this forum is your friend and will give you a lot of information on different methods.
4. Mites can live in the carpet. Getting rid of mites properly will require multiple treatments no matter thr method.
5. They won't bother your cats. Snake mites are just that.
Unfortunately refuting your research, and I say this with respect but also quite bluntly, I see no reason or benefit to cohabitate neonates of this species together, only risk and complication, such as transmissable health problems like ectoparasites for example. You most likely picked up some "hitch hikers" from the show.