that depends on the driving regulations of that county. Many countries only accept an IDP for a certain amount of time with the expectation that you'll get a license there if you intend to stay long term
every office is different. But the larger ones (Bangkok, Chiang Mai and Phuket) all allow 45 days. Even some smaller ones do like Hua Hin. But those 3 for sure.
You don't need a TM6 or TDAC. Leave it blank on the application form. Never ask another question to whoever told you that you would only get 7 days, because they are an idiot.
you absolutely did need to do a card on the plane. It was temporarily suspended a couple of years ago with all intentions to return (as it now has digitally). It was still being used at many land borders before TDAC system came online.
depends on if you want to add that much more time to your extension trip. I also don't know what would happen if you tried to purchase a re-entry permit when your extension is in an invalid passport if you tried to leave before your extension.