there is always the risk of injury and possibly death when feeding live and i can't say i'd recommend it here.
you heat the box with a UTH controlled by a thermostat and monitored by a probed thermometer inside, no lamps needed.
keeping ambient temps up depends on your own environment in the house. how are you measuring your temps now?
a good substrate will keep humidity well. something like coconut husk is fabulous for humidity and should work well.
tubs keep their temp and humidity very well.
for security: get a plastic storage container with a lid from target ($6). the lid has latches but i would put something heavy on top to ensure he can't push up any corners.
you'll need to make airholes in the SIDES of the tub. some people use a soldering iron but there are many ways to accomplish this. just make sure you don't leave any SHARP edges.
no offense but it seems you've been researching very inaccurate info. handling only applies to healthy and thriving snakes.
this forum is full of friendly people with DECADES of experience in keeping ball pythons. you should stay a while, there's so much you can learn just browsing here. you're already on the right track with asking questions and taking our advice. DON'T EVER feel like you can't ask a question; we're here to help!
keep us posted and ask us anything. 😀