Don't confuse the terms 'multiple entry visa' which is not relevant to your situation, with 'multiple re-entry permit' which is relevant. You can get re-entry permits (single or multiple) at immigration or airports.
It might depend on the office. I did it last week in Phuket, though. The statements contain the bank logo and all the same information as what you would get from the branch.
This is common and has been common for many years. I have read dozens of stories of the same. Particularly, the first time applicants are denied as a matter of course.
the clever way is to get a non-o before she leaves home. Banks will open an account here, with that visa. No insurance required with a non-o. Only an non-OA.
On a non O, you don't ever need to leave the country if you don't want to. While there are financial requirements, you don't have to provide any documents from a school or business when extending.