There are very few reports of people successfully applying for the DTV using a language school. Most will tell you to get an ED visa if that's what you want to do. But if you are going to be retired why not just get a Non-O based on being over 50? You can still study if you wish
As your embassy doesn't authenticate your income, they are only authenticating your signature, I doubt that there's any guarantee they will accept it. If they do they may also ask to see proof.
sounds like a retirement visa is the option for you. You could try for a Non-O based on being over 50 for one of you and a dependent Non-O for the other if your embassy will issue this. If not they may do so on a Non-OA visa. You need to check with them. You can only get a Non-OA in your home country and you can't get a dependent visa in Thailand if the primary visa is based on retirement. Failing that you would each need your own visas and you don't have sufficient finances for that
there are no restrictions as such but there is a requirement to attend school and study so leaving while you're meant to be at school is frowned upon and can result in you being questioned and potentially denied entry on your return
no it means that if you are entitled to you will get a fresh 60 days when you enter. If you are not entitled you will need a new visa (unless you are entitled to a 15 day visa on entry which you need to purchase)
but you can only extend inside the country one time then you must exit and re-enter. At which point you must report in person. Personally I haven't left the country for 3 years but have just renewed my passport. My online 90 day report was rejected and I now have to go in person