Pay the 1900 baht for a 30 day extension at your local immigration.
The likelihood of there being an issue if you don't is slim to non but the ramifications of overstaying could cause you plenty of issues in the future, not just in thailand but other countries too
Once you've been given your extension you can withdraw the 400k. You just need to make sure it's back in the bank 2 months prior to you next applying for your yearly extension.
Just open a bank account in thailand. You can do most things through wise but it becomes a massive pain in the arse if you are here longterm.
When she gets her ED-Visa her school should also give her a letter and be able to tell her which bank to take the letter too (if a language school) if its a proper Ed-Visa (university (Masters, Bachelor etc) then it doesn't matter what bank she takes the letter and student ID to as most will accept it.) However if it's a language school it's better to just go with the bank the school suggests.