You are not obligated to pay tax in any state in which you are not a tax resident. Somewhere your state tax board lists the criteria they consider when determining whether you are tax resident. If you have a home and/or business in the state then you are very likely a tax resident.
I stopped paying California taxes in 2019. This year the CA Franchise Tax Board sent me a letter saying that they noticed that I had not filed CA taxes in 2019 and that they estimated that I owed them $6,000. I sent them a copy of my Thai drivers license, My Thai pink ID card, and a copy of my passport showing that I had not been in the US more than a few weeks in the past 4 years. They sent me another letter saying they no longer considered me a tax resident.
I'm not sure if you consider yourself to have left that state but that is my recent experience.
If you have some kind of private Medicare supplement then it is likely they will cover you on a reimbursement basis.
There is no simple answer to insurance costs. It will depend on your age, health status, amount of coverage, and the deductible.
I am 68 and my policy costs about $2,300 per year with $300,000 coverage and a $1,200 deductible. This is probably excessive coverage considering costs in Thailand.