I had done the sandbox. They require you download an app to track your movements. The stupid app starting sending me message on day 7, I think. I got the test done on day 8 uploaded results day 9. The app would accept the results. Eventually I figured out I had to tell the app what day I completed the test and it accepted the results.
I just made the the trip a couple of months ago. It seems to me the US only required ATK, and nobody check my paperwork. However, my next flight back to US is through Singapore Airlines and they will require PCR within 2 days.
You will need to check your airline's requirements. You may even need to concern about your transit country.
From Los Angeles Embassy it had taken me a couple of days. It all depends on which embassy and how busy they are. The visa was quick and painless, the Thaipass was another matter entirely
The price is determined by how much they can get from you. Safety wing changes price depending on your age. AXA does not. AXA doesn't change price depending on age, or country of origin ( I checked a few countries), vaccine status or health conditions.