I know you get a certain amount of attendees based on the groups attending and their influence, but does the date of your show matter, or does the system compensate for that?

The system compensates for it. If your show is 10 days away and you're supposed to have 300 attendees you'll get 30 each day.

But since the groups attending the competition have an ever increasing influence, is the number of fans buying tickets just based on the group's influence when they apply for the competition, or does it increase as the group's influence increases right up until the day of the competition?

The total attendees for each event are calculated daily based on influence amounts at that time. It will change up until the day of the event. However, it generally takes more than one day's worth of influence changes to increase the total attendees, so you might not see a leap in new attendees from today to tomorrow, for example.