That will depend on the embassy. Some embassies might accept it, and some might not. Some might require double the amount of funds if they do accept it, since only 50% is yours.
You would want to contact the facility to find out. They are the ones who would be responsible for applying for the visa with paperwork from a doctor, so it would be up to them if they're willing to do it and if they know of the process.
As of July 2024 the limit was removed. There is now no limit cited in any policy. But that doesn't mean it's unlimited. Every entry is at the discretion of the immigration officer you are standing in front of, and if they feel you're not a tourist and/or you are abusing short term entries by trying to stay in Thailand long term, you'll be questioned and possibly denied entry. Many reports of this happening to people after only a single 60-day visa exempt entry with a 30-day extension.
Depends on the embassy or immigration office. Some might have a policy of requiring someone 50 or over to apply for a retirement visa instead, since you can study on any visa.
You will need your passport and your TM30. If you live in Pattaya you cannot report in Bangkok. You must report to the immigration office that matches the province of your TM30.
Some embassies will accept as long as it says you can work remotely internationally. Some embassies will require the letter to specifically say you can work remotely in Thailand.