If you have a return ticket within 30 days of arrival, you'd be fine with 30 days of insurance. Most people book a refundable ticket and then cancel it after they arrive.
No, you need an appointment. You also don't need the "vaccine passport" to travel, proof of vaccine both digitally and on paper are accepted everywhere.
I don't know anyone still waiting for their first shot. Anyone over 18 is able to walk in now for shots, don't even need appointment in Chiang mai anyway.