AXA is Thai insurance and will cover hospitalization for asymptomatic positive cases (as far as I know), whereas international insurance such as Safety Wing won't. That's the benefit of a Thai insurance policy, whether it's AXA or not. Whatever you decide, just confirm with them first that they'll cover for asymptomatic hospitalization in case you test positive, or else it will become very, very expensive.
Yes, the fever on arrival wouldn't be great, nor would the combination of jet lag and other possible vaccine side effects. If possible, I would do it a week or at least a few days before you depart
Yes, but unlike a plane, it's possible to get into a van by myself. And getting into a van with others is doubling my risk of getting quarantined...why would I do that if I could avoid it? Risk management.
Just for the future, you can convert your pdf to a jpeg by choosing "export" (this is in Adobe, but others should have the option), and there will be an option for jpeg..super easy. Good luck! :-)