Take your girlfriend with you.. And her blue book. Probably the easiest way. Usually banks tell you no at first, persist, keep handing them documents and usually they say yes... But with your gf, will probably be easier. If you get a firm no, go to a different branch.
you don't technically need a fixed address. You just need a resident certificate. Some immigration offices require a lease agreement, but Bangkok it's usually just 90 day report filed.
The US Embassy does not care. You can put any address you want. Some embassies require verification though.
That address will be in the book of course, but I don't think it really matters 99% of the time.
Seem like probably untrue.. An embassy requiring a bank account from Thailand for a tourist visa.. Most tourists should not a bank account and first time tourist would have no way to get one.
You talking to an agent or a visa mill school right? They want to up sell you on a retirement visa. If you you want to just stay here, get a retirement visa, don't use a visa that could get you in trouble. If you want to learn Thai find a more legitimate school.