Happy to help!
1. You might be able to remove the existing he's mat if you're careful. The have thin coils in them that create the heat which are fragile though when bent.
Otherwise, yeah a new one will be needed. I can't say with 100% confidence you can leave the paper on, but believe you can. I don't want to steer you wrong though, so please double check.
2/3. Your temps are spot on. But yes, you'll need a tstat for the CHE. You can use a rheostat (dimmer switch) but it's not accurate like a tstat. You need to adjust as room temps fluctuate. Whereas a tstat does the work for you.
A temp gun is a fantastic tool every keeper should have. Remember to temp the actual glass surface, not the substrate because your snake will burrow and push substrate around. The kids will have fun temping things too!
4. I know it's tempting to hang out with a new pet, but unfortunately snakes are a bit different that way. During your research I'm sure you learned BPs can be a bit picky about eating, which can be true. The two major reasons a BP will refuse food are improper husbandry and stress. You're already nipping stress in the bud by cluttering the enclosure, but handling is obviously stressful for them. Since new keepers can't easily identify stress or troubleshoot it's best to avoid stress altogether. It'll be worth the wait.
5. I personally only use a humidity box during shed, and not with all of my snakes. But it certainly can't hurt to offer one all the time. Plenty of keepers do.
Good luck! Please keep us posted. Feel free to ask any questions you have, we're happy to help.