Is it a PVC cage? If so, best bet would be to get a RHP. Then you can ditch the UTH or at least I don't use UTH with a RHP and I don't think Mr Misha does either. Think a lot of others do though so its up to you. If its just a screen top cage, then probably a CHE. I use a CHE in my 36x18x12 glass tank for my BP but I also use a UTH since it is a glass tank. In my Pro-Line 48x23x14 I just use the RHP on a Herpstat.
Lighting is fine if you want but I wouldn't use some intense crazy bright lighting. Just something like leds or fluorescent tube. I have my BP glass tank close to my bearded dragons and BCI cage so she gets ambient lighting from them. In my BCI cage, the Pro-Line, I only use a 18" T8 4500k daylight tube. Its really up to you but as far needing light, no a BP doesn't need lighting in their cage, its more for the owner.
No, it's not a pvc. It's a glass terrarium. Does the Che need to be on a thermostat?