You'll get different answers at different banks. None of them are on the same page, seem to make up their own rules, and it depends on who you talk to, or if they're in a good mood.
We were told once at Bangkok bank, that we needed to bring the Puu Yai (headman) of our village to vouch for us in order to get an account! The guy is always drunk, and requires whiskey and 1000 baht for him to go to the bank with you. If he has a wreck on his way there (1.5 hour drive), you'll also be responsible for damages.
We ended up opening an account with Krungsri (yellow bank).
Yes. The money must be in a Thai bank and age (at least 3 months I think?). It must stay in the bank almost year round. I think you can withdraw down to 400k, but I'm not sure of the timelines here.
You'll have to get a certified statement from your bank as well.
I'm sure others will chime in here with clarification or corrections.