1. I am not sure how big that tub is but you will need a heat mat that covers 1/3 of the floor area of the tub. Mount it to the outside of the tub using aluminum foil tape (found at the home depot).
2. Yes, they are mandatory. The reptitemp 500r is the cheapest model at about $25. Unfortunately, they are hard to find in stores and you will most likely have to buy it online.
3. You don't need space between the heat map and the container, but you do need space between the heat mat and whatever surface it is sitting on. Most UTHs come with little rubber stoppers you can use to prop the tub up. You only need a small space for some air flow. You should have two identical tight fitting hides and a water bowl in the tub.

hope this helps