I think Scubaf250 was thinking you are using a tub in a rack system not just a tub by itself.
You can use the uth but will need a tstat. A far as lamps go, that depends on the temp of the room the snake is in. The uth will create the hot spot but the rest of the tub will need to be around 80. You keep lamps from melting things by using lamp stands. Laying a fixture on the tub or tank is not the correct way, is the cheap and easy way. A lamp stand ($30 at both big name pet stores, ZooMed) gives you the added ability to move the lamp up and down therefor raising or lowering the temp as needed. Stands will also extend the life of the bulbs because your not knocking them around moving them off and on.
If you decide to use a adult size tub for a young bp be sure to give it fake plants and plenty of cover so when it moves around from hide to hide it will feel secure. If it doesn't feel secure you will find yourself dealing with a stressed snake.
What's the sanitary reason for feeding in another tub. You think mice are dirty? Remember that even when feeding f/t your snake will usually wrap it up to make sure its extra dead. Mice and rats are part of the hobby and feeding in another tub is just not needed. You would have to clean the snake after feeding to really be rid of anything you may think is on the prey and that will certainly cause stress and a possible regurgitation.
Using humid hides is fine if you have naturally low humidity. I use them.
Feeding weekly is fine.