Almost impossible to open a Thai bank account if youenter this way on a 60 day visa exempt entry. Without a bank account you cannot get a retirement visa. Best to get a Retirement visa from your own country before coming to Thailand.
You had a visa exempt entry and not a visa on Arrival. The title documnet for land (and or house) does not help you. You would need your wifes Thai Id and possibly her house book (address registration).
Your biggest difficulty will be to open a bank account in Thailand which (even with paying an agent) is almost impossible unless you have a long term visa. If you want a Retirement visa it would be best to get it in your home country before you come to Thailand.
3 visits to Thailand this year would indicate to Immigration that you are no longer a tourist and I suspect that Immigration will require you to enter with a long term visa appropriate to the reason for your stay. If you attempt to enter on a visa exempt I suspect that you would be denyed entry.
You cannot renew a retirement visa. It expires at the end of its term. I suspect that prior to your visa expiring that you obtained an Extension of Stay based on being over 50 years of age. That is not a retirement visa.
For Australia, you really need a well prepared application. My has has had two approved tourist visas and I had no difficulty obtaining a tourist visa for my daughter.
As an American passport holder you can arrive in Thailand without having a visa. At the arrival airport the Immigration officer will give you (currently but planned to reduce at a future unknown date to 30 days) a 60 day visa exempt stamp in your passport.