It's not a tourist visa, it's an education visa. Whether the bank will let you open an account or not is up to them. Many reports of people with ED having issues.
The official rules are that you're taxed on money remitted to Thailand if you're a tax resident. Income sourced outside of Thailand doesn't mean you sent it to Thailand. It's much more complicated with dual taxation treaties, but money earned does not equal money remitted.
I've also heard reports that some people see the correct code on the Thai language statement but not on the English statement for some banks, as odd as that sounds.
I've always been unclear if it's 3 months after the extension is issued, or if it's 3 months after the date of the extension. I always say date of the extension to be safe. But if they take it 3 months from the date the extension is issued, you might be okay.
once you apply for the 1-year extension in Thailand, you can purchase a multiple re-entry permit. But there's no multiple entry visa available. It wouldn't matter anyways since the visa is only a 90 day visa