Welcome back to snake-keeping. I'd personally use that 10 gal. tank too, with the modifications suggested. And "FYI"- many BP-keepers here prefer to use 'tubs'
or the professionally-made plastic enclosures, & that's fine...there's more than one way to do things, but like you, I prefer glass tanks for my snakes (which these
days are not BPs) but as long as you achieve the same results, it's up to you. Humidity does not escape thru glass OR plastic, it's a matter of how much air
circulation you allow. Many find it helps to cover the back & sides of a glass tank also, especially for a shy species like a BP, & especially until they settle in & eat. If your house or room is on the cool side, there are various materials that you can insulate a tank with also...& if you put scenery (on the outside) first,
it will look nice & you'll never see the "insulation" (foam board etc etc)
Placement of snake cage: living rooms are fine if not too "busy". Don't put a snake cage near TV/stereo, or near doorways & windows (where sun streams in).
You may find it's better to start off with tank in a quieter room, then move it to living room after the snake is settled in & eating regularly. Snakes are shy & afraid.
Size of UTH- typically about a third of the floor space, yes...but keep in mind how warm or cool you keep your house, and compare that to what your BP needs.
They do need to have temperature choices to properly thermo-regulate themselves. It takes some experimentation (best BEFORE the snake is living in the cage)-
we recommend setting up the cage a week before occupied so you can check that the temperatures are correct & make any changes needed. Sometimes things
don't work as planned.