If your school knows what it is doing, then a work permit renewal should only take a day or two - provided there are no unforeseen problems. 

Yes, as long as you have a non-B visa which entitles you to get a teaching licence and work legally in Thailand.

You can then obtain a non-O visa for your children or spouse (qualifying them as dependents) 

I've never heard that there is an age limit for a visa, but 60 is apparently the age where you can't get into the social security scheme.

In my experience, there is no problem getting a work permit after you turn 60.

(Thanks to Terry LH for answering this question)

An ajarn reader writes - "I came into Thailand a week ago on a non-B visa with the intention of working at a school here.

I discovered on the first day that the terms of employment were not as they appeared to be. I informed the school that I would not continue with them and that I would need to look for other work.

Naturally they were not pleased and said they would go to immigration and cancel my non-B. Can they do that? Please help!"

Phil says "I'm not getting the full story here but I assume you fixed up a job while you were still in your home country and the employer sent you a letter of 'intent to employ' and you used that letter to get a non-immigrant B visa at your local Thai embassy.

The truth is that you haven't done anything wrong. It's not your fault that now you are actually here, the job has not turned out to be what you expected. 

It seems I can never repeat this enough but NEVER fix up a job before you arrive. Wait until you get here and then start looking for jobs.

Back to the original question - the employer can't waltz into immigration and start demanding that visas be cancelled. There's no contract between the two of you for starters. It's nothing but an idle threat. A pretty nasty one at that. I'm sure you've learned a lesson or two from all this though.  

It's actually not a requirement to bring a criminal background check document (CBC) to Thailand, although some employers may ask to see one. 

The vast majority of employers have realised that generally teachers arrive in Thailand without the CBC and getting one from their own country or state is just too time-consuming and too much hassle.

The real problems can occur though when a teacher goes to a Thai embassy or consulate in a neighboring Asian country to apply for a non-immigrant B visa on the basis of obtaining work as a teacher. At some embassies and consulates, they will ask to see a CBC. Not all of them but some.

Getting yourself a CBC while you are in your own country is always a wise idea. There's every chance you won't need to show it but always be prepared for a first time.

The fact that you've been in prison for the crime committed (information withheld) won't matter.