Australia has a very preferential tax treaty, in that all forms of Australian pensions are not assesable in Thailand. This is not true any other country where it's typically limited to government pension only.
yes, you are correct, but... Although, DTA typically requires credit system under the international treaty, most countries still have a foreign tax credit under domestic tax laws in place even without a DTA. Thailand doesn't actually have a formal credit system, the RD department has is instructed to accept adhoc. Part of the changes last year, the RD was supposed to be working on a credit system and it would likely apply to all countries regardless of a dta.
yes, but you are still taxed by both. It's a common misconception of tax treaty that you will only be taxed by one which is what the OP question was about.
It depends on where you are. Some amphurs are impossible for foreigner to get a yellow book and other very easy. In general though, it's fairly hard to get.
Your child can enter as a tourist/exempt and then overstay without penalty. The wife is the issue (they always are). You can leave her behind, or she can get her own visa. Depending on how long she might be able to play the bounce out game.
not an expert in schools, but I have noticed there pretty decent international schools in most areas. Maybe not top tier, but good ones. I doubt you would have trouble in Rayong.