In order, just off the top of my head without reading the link;
Yes (because as noted, it doesn't kick in instantly. It can take a couple of weeks or more), yes (because if you are infectious now it will still take time for the vaccine to kick in and help out, and it might not help that much), probably on the lower priority list (if the vaccine carries multiple strains you want them immunized for all of them instead of just the strain they caught), it may or may not help and/or worsen the situation, given how nasty COVID is expect 98+% of the population for herd immunity, generally you don't want to mix vaccines (it could work in theory but the odds for it are laughable).
Yes (because as noted, it doesn't kick in instantly. It can take a couple of weeks or more), yes (because if you are infectious now it will still take time for the vaccine to kick in and help out, and it might not help that much), probably on the lower priority list (if the vaccine carries multiple strains you want them immunized for all of them instead of just the strain they caught), it may or may not help and/or worsen the situation, given how nasty COVID is expect 98+% of the population for herd immunity, generally you don't want to mix vaccines (it could work in theory but the odds for it are laughable).