If it's an airline rule and they don't let you board, your Thailand Pass may be irrelevant. I'd make 100% sure. The airline may put that rule in place to avoid controversy with a potential unvaccinated traveler testing positive and forcing nearby vaccinated travelers to quarantine (yes, I understand the complexity and irony, but trying to see their "logic")
Must be different types of Non-O. I'm on a Non-O volunteer (with work permit; visa originally established abroad) and have never had to show bank statements.
Probably only the consulate could you tell absolutely, but I would think not.
I came in on Test & Go (though applied under CoE) with a re-entry permit (non-O). The passport control agent basically asked if I wanted to use that or do a tourist visa (since my non-O was expiring soon). I stuck with the re-entry since I knew I'd be renewing soon, but he didn't care about what the pass was granted under.
Traveling together can use 1 room. There's no reason to keep separate as if 1 of you tests positive, my understanding is all of you go on quarantine protocol.
With "Exemption from Quarantine (aka Test & Go)", it's 1 night OR negative result. You should be free to venture out now. Sadly, it sounds like the hotel doesn't have accurate information, but maybe their own process it different with their certificate.