You don't have any visa at all right now, so you cannot get "another visa."
You can go to your local immigration office and apply for a 30-day extension one time. Or if you want you can leave Thailand and return to get a new 60-day visa exempt stamp. Some Laos borders require you to stay in Laos 1-2 nights if you're trying to enter Thailand without a visa.
all wrong. You can't apply for an extension of DTV since you didn't enter on it. And the DTV extensions costing 10,000 was only a rumor and we know now it's the normal 1900 baht for an extension. But most immigration offices make it impossible to apply for DTV extensions so you're better off just leaving and returning every 6 months
you can apply in Thailand. But one of the requirements to apply is showing you have 800,000 baht in your Thai bank account. You cannot open a bank account as a tourist.
with the non-OA, some immigration offices might allow it and some might not. It's very difficult to plan around it because if you ask at the beginning of the 1-2 years you can get with the non-OA and then go to make the switch after you've been in Thailand for 1-2 years, the answer might have changed by then.