If you go to enough branches, you will eventually find one that doesn't know a DTV is a tourist visa. I opened my first bank account with a visa-exempt stamp. The girl said she needed a photocopy of my visa, so I pointed to the entry stamp on my passport. I still have this account. It helps to be outside of popular tourist areas.
It starts when you enter the country. You do your extension at the end of the non O 90 days, so it counts as a report, and your next 90-days is into your 12 month extension.
A single-entry tourist visa is for 60 days, but can be extended for a further 30 days at a cost of 1900 baht. A multi-entry visa is valid for 6 months, but every 60-day entry can be extended for 30 days for 1900 baht. If you time your re-entry correctly, you can stay for nearly 9 months.