+1 on everything Bogertophis said up there, including not being entirely gung ho on to offering UVB (especially unmetered UVB, I'll add) to a species that doesn't require it.
I'd look at all this more as improving your practices rather than 'doing it wrong'. We can all improve, all the time.
I've had good luck with such products from Acu-Rite. I've not had long (or even medium) term success with pet-marketed electronic accessories (Zoo Med and the like).
Not necessarily, but it wouldn't hurt. The most useful readings will come from an IR temp gun (they should make them with a belt holster so they're always at hand -- only half joking here). I have a thermometer in some enclosures just as a sanity check, but most I don't. Keeping an eye on the snake's behavior can tell a lot too -- if they're avoiding the warm side, or always hanging on it, that's a clue.
Without knowing quite a bit about how wild BPs regulate their temp during nocturnal activity, I'd be hesitant to give much of a night temp drop, especially beyond the background temp drop the enclosure will experience simply from being located in a human house. I poked around Google Scholar and couldn't find any good info on BPs nocturnal activity as related to temps. It may well be (like leopard geckos, who shouldn't be provided much of a night temp drop, if any, contrary to some claims) that they stay burrowed up on cooler nights, or they may limit the duration of their excursions so to go warm up often. Continuing to offer a typical temp gradient no matter what time it is will allow the snake to regulate its own temp as needed. Unless the keeper has a real solid understanding of why they're forcing something (like cooler temps) on an animal, it might usefully be assumed that the animal knows best how to take care of itself and will do so if given the options.