Almost every immigration office requires you to file tm30 if you reenter the country. I believe chonburi is the one exception. Just because you didn't stay overnight doesn't matter. When they look you up they will see you last entry was later then your last tm30 file.
You get an ED visa from a school... So check schools not agents.
Probably not a lot of informal schools in Buri ram (Thai Ed, Muay Thai), but you can check. Otherwise you will have to go to university of you want an ED visa.
in the history of the law, no Thai person has ever been fined. It is always passed to the foreignerto pay in order to do 90 day reports, extension, or immigration processes.
For the online system? Book and title deed in addition to your list to setup an account. Then for foreigner passport data page, visa, entry stamp and tm6 (if have).
File by mail. All of the above as copies plus application and return postage envelop.
The nonthaburi​ should issue them, they did in the past and they are supposed to. You might have had a misunderstanding. I also believe they do require a 90 day report same CW office.
Work is work regardless. Even working for a foreign company that has no presents in Thailand is still not allowed. However, it's typically seen as a grey area and immigration has said it not something they activity enforce unless their are problems.
Walk to a different branch. Many people open accounts on tourist visa. Tell them what you are doing and bring many documents...its usually a bit of negation..search the group for bank account posts... There are many.