To apply for a Non O visa in the USA you do not need a Thai bank account and you do not need health insurance. You just need to show a minimum balance of $
*****
in your US bank account.
When you get to Thailand you can open a Thai bank account and transfer the
*****
0 baht into it ready to get your first annual Extension towards the end of your 90 day initial stay.
You do not require Health insurance for the extension on this visa.