that's 4 out of 60 odd DTAs, I'm not going to check any of them specifically but I know many of them only give a pass to civil service pensions. Even the state pension is taxable under the UK DTA. Sweeping statements are the biggest issue, everyone needs to check their own situation
Paying tax is nothing to do with whether you have a kid attending school or not. The starting point is spending 180 days or more inside Thailand which makes you a tax resident, visa is immaterial. Then you have to look at whether you bring assessable income into Thailand in that year and if so you need to file a tax return if it amounts to more than 120k baht. If you pay tax elsewhere and that country has a DTA with Thailand you can claim a credit on the assessable income you bring in for tax you have already paid on that income
The Non-B makes sense as that is for working inside Thailand. I can't see other visas being tied to immigration as there are just too many variables for immigration to get their heads round.
SS is covered for a US person but that doesn't mean all pensions are. Most of the DTAs do cover pensions earned in government service so civil service, military etc
If you are on an extension of stay then that extension finished with your contract, you should have cancelled both your work permit and the extension on your last day of work and left the country.
If you are on an actual visa (check your passport) you can stay until the visa expires
I've been here 8 years on long term extensions and last I checked they won't give me one. I'm not married and don't have any property though which is what counts me out, at least at my amphoe. To be honest I only tried to get the book in order to get the pink ID card but I find a driving licence is just as good in most situations
You can show money in your Australian bank when applying for the 90 day Non-O visa inside Australia but to get the 12 month extension inside Thailand you will need to show funds in a Thai bank, seasoned for 2 months before you apply
if you want to be pernickety you can go through all 60 odd dual tax agreements and find different exemptions in each one. But the basic principle that income is taxable whether or not you are retired. It applies to income earned inside Thailand and it applies to assessable income remitted to Thailand from elsewhere