It's Embassy-specific. In some you can in many others you can't. For example, when I applied for my DTV in South Korea, only Korean citizens or non-Koreans with residence cards could apply, but no just visitors or tourists. This was in August last year. Rules might have changed since (as you see, they keep changing the rules every time).
yes, owning a property, having a long term visa/work permit or being married to a Thai national. Without any of those you're up to the luck of the day, but if any of these three, you're totally "safe".
Yes, leave the other unpaid, it will automatically disappear from the system in 14 days. You don't need to wait for it to disappear to create a new application, and pay. The Embassy will see and review only the paid ones.
I won't argue that it sounds like a stupid rule, but, nothing that a short (like same-day) trip abroad can't solve. You can take a flight in the morning, then come back in the evening, and voilà, you get 180 more days.
Participante anónimo 987 yes, and by the Thai authorities themselves, the DTV is "not" a long term visa (I know, this doesn't sound about right, but legally speaking, it isn't one)