Everything sounds fine,
I definitely recommend a UTH, heat lamps just zap the humidity which sucks. When you get a UTH, I highly recommend ordering a thermostat http://www.reptilesupply.com/product.php?products_id=75 , ReptiTemps are the cheapest and are pretty reliable. If you do end up getting it I could help you out on how to set it up, just send me a PM.
Try keeping the heat lamp on one side of the enclosure with the hide you currently have and get another identical hide to put on the cool end. Snakes need to thermo-regulate which means they need to switch their body temps from going to the hot end to the cool end and vice versa. Having identical hides is essential, if the snake prefers one hide over the other it will not want to go into the other to thermo-regulate.
Pinkies are much too small for even a baby Ball python. Try feeding something larger like fuzzies or hoppers depending on the size of your BP. If he eats one fuzzy and there really is no slight visible bump in the snake then you can feed a second fuzzy to him if he'll take it. Sometimes you may just have to feed two fuzzies if one hopper seems too large.
Also, make sure the rodent is pretty warm after you have thawed it out. Some snakes just won't take a rodent that is too cool.