We were there on 11, 12, and 13 April this year. We got a VQ on each day (TP had IOA predicted as CL 9 days, though rain cleared out folks on 11th afternoon and TP indicated the other days were actually a 6 and a 7 with USF being 8s). Sunday we got a VQ ~1735 when someone else called out excitedly in Leaky Cauldron. I had enough time to hop on and get one for around 1845 (USF/IOA Trip Report (11 Apr 2021) Sunday afternoon). The other days we got one in the mornings ~0840 (links to those trip reports are found in the other posted link).
1- My understanding is that, yes, VQs open when the standby line reaches a certain point, which was ~0840 on days the park officially opened at 0900 for offsite folks.
2- Unsure about push notifications. I just checked manually.
3- I think by crowds, as the Sunday late afternoon drop occurred because Hagrid’s came back up after a ton of rain.
4- No actual idea, but I took it to mean for the rest of the day (unless extenuating circumstances - like the storm)
5- Yes, we specified how many in the party, but not who. This would allow two different phones to get seperate VQs.
6- I agree with you that Hagrid’s is the best ride in Orlando/Lake Buena Vista area.
Have fun on your trip.