yes, I originally applied for a Non-O visa based on marriage online in the U.S. and all I needed to send was a pdf file of my investment statements. So yes, the money can be in an account abroad.
you need to have your US document certified in Thailand. The U.S. embassy is the only place Thai authorities will accept. Then you have to get it translated and get that translation certified by MFA in Chaeng Watthana. Then you can use that certified translation whatever you need it for in Thailand (Amphur, immigration etc).
you can not overstay the length of your non-O but it is clearly not 90 days per entry. The only thing that happens after 90 days is that you file a report.