How busy are the parks?
Very. You are in peak time. It's not like you cant move, but wait times do go up, and dining is harder to get.
How hot is it?
It Florida in the summer - it's hot. I have seen it 80's, I have seen it high 90's - it depends on the weather. It WILL be humid however, and it will most likely rain every afternoon (wait it out in the parks, most summer storms in FL are short)
Anything special that we should go do or see in terms of the fourth?
People have already told you about the fireworks at MK and EPCOT
And is anyone else going? More specifically is anyone staying at the Grand Floridian during that time?
We will be leaving on June 30 (and staying at BWV anyway). However, the MK fireworks on the 3rd and 4th are all around the perimiter as well.. During these shows they shut down the roads around MK, including the roads to the GF. You will not be able to get in or our of GF during the show times, so plan accordingly. The GF does play the audio for the MK fireworks on the speakers at their boat dock, so you can go down to the boat dock and watch them there if you want. However, everbody in central Florida who does not want to go INTO MK also has the same idea. It's nowhere near as packed as MK will be, but it will be a lot of people. Any Disney Springs busses out of GF after the fireworks will be packed to the gills. Last year we ate at Narcosses and then walked down and watched the fireworks on the 4th. Again, a good number of people, but nothing crazy. We were staying at OKW that time, and instead of waiting for a DS bus that we could actually get on (they were comming in packed from the previous stop at the Poly) we went AK and transfered to an OKW bus there. Much faster. Of course, you will be able to walk to your room, if thats what you want to do.
-dave