anyone can get a residence certificate. It's just based on the reporting that your landlord or hotel do, telling immigration where you officially live. Most agents will get you one next day for 1500bht
in pre covid times I used to fly in on visa exempt every other weekend. Never an issue and once I asked and was told as long as you fly in and out each time (and not a bounce where you just come straight back) unlimited entries. But that is precovid....what the future will be is unclear
Surely you need same as everyone else entering Thailand, as required to get the CoE - which won't cover your treatment as this is preexisting. Just buy the basic insurance for period you here to tick the box on entry