Hi there! Welcome to bp.net!

First I'm gonna strongly suggest you read the caresheet for ball pythons - that will answer a lot of your questions.

There should be a temperature gradient - approx 90-92 on one side and approx 82-84 on the cool side. You are going to want to measure these temperatures on the ground (where the ball python will be) with something like an Accurite thermometer (you can get them at walmart for $12) that has a probe you can put under the hides to measure the temps there.

Bathing isn't neccesary, really. If your BP is soaking alot it could be before a shed or you should even possibly check for mites, since sometimes they will soak a lot if they have mites. If you do bathe your snake you want the water to feel lukewarm/cool to your touch, no hotter than that.

An UTH is an under tank heater - so its like a mat. (but don't use a human heating pad since they aren't meant to be left on 24/7 and it will likely overheat). You really want a thermomstat or at least a dimmer on it becase you'd be amazed at how hot they can get.

Why don't you post pictures of your set up and you can get some really great advice from the people here on your setup!