I don't know about that insurance specifically, but I just sent in the basic coverage letter (1 page outline with names of covered people and general policy info) NOT the actual policy document.
It can be booked under your name, but contact the hotel and ask for a SHABA certificate. They'll then ask for the Names/passport info for the people staying
They'll consider it based on flight time, not application. I wouldn't worry about that. As long as you've been in the US longer than 21 days (i think?) by the time you fly.
I had everything printed (and would still recommend everyone do so) but they only looked at CoE & pre-flight PCR in addition to the passport & arrival card.
They never asked for T8, Shaba Cert, vaccination card, PCR test results or insurance. Had all those ready, though.
Sharing should be fine. You'll likely need a SHABA/AQ cert for each person, but it can be under the same booking (make sure to clarify with your accommodation)
"Exemption from Quarantine" scheme says "1 night OR negative test result."
I suppose it's a bit nebulous what "1 night" means, as someone could stay over the midnight hour, but at least you can presume much less than 24 hours.