It's hard to say at this point what will be happening at that time of the year. My guess is that the weekdays will be better than the weekends (usually) and the summer crowds probably won't have started arriving yet. You might see some residual crowds from the Marathon weekend early on during your trip.
There are few different crowd calendars that get mentioned here on the Dis and it's usually worth looking at all of them to get a
sense of what the crowds
could be like. If all are saying it'll be crowded, then it'll probably be crowded. If they're split, then I generally think that means no one really knows what it'll be like.
Grad Nite is an after hours event in DCA, so assuming things stay the same this year, it won't impact on the parks' operating hours. The Grads are given park hoppers, so you'll find groups of high schoolers in both parks all day long. The last time I was there, I did notice an uptick in Grad Nite attendees as the day progressed (basically, as they arrived). Some Dis'ers have had awful experiences dealing with the high schoolers, others have said they didn't have any problems. There is really no way to know in advance if you'll come across any "badly" behaving groups. I thought that they did add to the crowds at the thrill rides and nighttime shows (especially in DL), but that they behaved pretty much like any other group visiting the parks...some were better behaved than others, but the same can be said of any group.