You didn't miss anything. A 90-day report is for reporting 90 consecutive days spent in Thailand. If you were not in Thailand, you were not spending 90 consecutive days in Thailand. When you return to Thailand, you start counting again at day 1, because it's only 90 consecutive days spent in Thailand.
When you go to get your extension, they might do a new 90-day report for you, and they might not. If they put a slip of paper in your passport that gives you a new date to report for your next 90-day report then they did one for you. If they do not put any paper in your passport, then your report will still be due 90 days from the day you entered Thailand.
Completely depends on your immigration office. Most want a new TM30 every time you re-enter Thailand. Some even want a new TM30 every time you travel within Thailand. While some don't need a new one for either as long as you return to the same address.
First of all, give up on any idea of extending the DTV. It's almost impossible and even if you do manage to do it, you'll have to take so many trips to immigration and spend so much time in the attempt, that you won't even bother next time.
Just do a border bounce when you need more days. You're not required to spend any amount of time out of the country. You can cross a land border, turn around, and re-enter immediately for a new 180 day stamp. You can fly back same day if you can find a flight schedule that works.
Immediately travel to the country where the application was submitted and hope they don't discover it or they'll cancel the application with no refund.
No one can say for sure. But it's more about the total time in Thailand than it is about number of entries. Generally people start running into issues once they've been in Thailand for 90 days in a 6 month period, and 6 months within a 12 month period.