Depends on the bank. I opened my first bank account with just lease document. Most user friendly bank in Bangkok is probably the Bangkok Bank Head Office branch in Silom. They have an international section on the second floor where they all speak English
The TM30 is a "Now" document, but the problem will be with the certificate of residency as I don't believe immigration will allow one with a hotel address, and the certificate is actually posted to the address
All the things you want to do you will most definitely need a TM30. A quick fix is to book a night at a hotel and get the screenshot printout from there
Unfortunately Thai immigration don't do "introvert". You can do learning online but not with an ED visa. You can get the 60 day tourist visa, which you can extend a further 30 days. There's nothing to stop you signing up online under this visa