Genuine approval will have the QR Code certificate. If they do need any information it would be asked to be done via the Thai Pass registration form not over email
You should be picked up from the airport by the hotel , straight to the hospital then to the hotel where you stay in your room until you get your test result
I would play safe and get a Thai approved insurance like AXA some travel insurance companies only cover you in the case of showing symptoms not just a positive test. Fine print is everything. Also if staying for 2 weeks get insurance for 1 month to be safe