During and around Aoi Matsuri time

I am trying to find out whether or not the shrines that are a part of the procession will be available to visit and still have scheduled tours on May 15, the day of the Aoi Matsuri? I'm trying to kill two birds with one stone so if we were to purchase tickets to view the procession from either the Imperial Palace or Kamigamo Shrine in advance, can we then schedule a tour prior to or following the parade or will we have to go back to see them? Is it worth purchasing tickets or should we just watch from along the procession route?

Typically, on this day and the days prior and following, is Kyoto a busy place? Will we be visiting the shrines and temples with the rest of Japan and other tourists?

Many thanks like always.

I am trying to find out whether or not the shrines that are a part of the procession will be available to visit and still have scheduled tours on May 15

The Kamo Shrines are open except during a few hours around the time when the procession is passing through. Tours of the Imperial Palace are never held on Sundays.

Is it worth purchasing tickets or should we just watch from along the procession route?

I don't think it is wort the effort. I would rather go to the Imperial Palace 60-90 minutes before the beginning of the procession, get some good viewing positions in the front row and see the procession from there. You could also see it along regular streets, but the surrounding atmosphere is much better in the Imperial Park.

Typically, on this day and the days prior and following, is Kyoto a busy place?

The festival has not a great impact on how busy the city is, especially not on the prior and following days. A much greater impact has the weekday that the festival falls on. It is a Sunday this year, which means that you can expect it to be rather busy. Kyoto is always busy on weekends.