1. Depends on your household humidity, but i would go with cypress.
2. Ultratherms have been great to me, so i would go with them and purchase them from ReptileBasics.
3. I would see if a Ranco would be in your budget. $60 and its a very good thermostat for the money.
4. Yes i use all sterilite or iris tubs and have no issues when i regulate the heat pad with my ranco thermostat. The actual heat pad shouldn't have to be anymore than 105 to get the appropriate 90-94 degree hot spot ball pythons need. That is not nearly enough to do any damage or warpage.