1) Just ask hotel for proof of your TM30 if you need it
2) assuming you have a non-O based on retirement, you need to open a bank account ASAP and transfer your 800k. You might need to get the TM30 from the hotel and go to immigration to get a residence certificate for bank account. While you're there, ask them for their handout for the 1-year retirement extension.
3) Kasikorn or SCB
4) Rental agents are specialized by area. So you need to find an area you want to live in first then find agents that know that area.
Then you were applying for the wrong visa if you needed a signature from your doctor. Only the 1-year non-OA visa needs that. What you want is the 90 day non-O visa that doesn't require insurance, a medical certificate, a background check, or any of that stuff. And no, you would not be able to switch to a retirement visa by presenting it to anyone except passport control as you enter Thailand.
What you got in the past was a tourist extension. That means you entered Thailand as a tourist, either with a tourist visa or no visa at all and entered visa exempt. This time you did not enter as a tourist, so you cannot get a tourist extension
Which extension were you trying to get? A non-O based on marriage can only be extended 2 ways:
1) a One-year extension based on marriage to Thai, including proof of funds in your Thai bank account for 2 months, and a large number of other things which varies by immigration office
2) a 60-day visiting Thai family extension based on your Thai wife. Not all immigration offices offer this extension.
For both of these, your wife would need to be with you and your marriage would need to be registered in Thailand at an amphur office.