My general sense is that the last week in April shouldn't be a hugely crowded period of time in the parks, mostly because it's after Spring Break Season and before the Summer Season gets started. That being said, the 60th Anniversary Celebration has seemed to really increase the crowds in the parks, so no one knows how that will likely impact the parks in 2016. At this point, the only "event" that I've heard about is Bats Day in the Park (
2016 Calendar) at the end of April, but more things are likely to be added. As
SMD said, you're likely to encounter some refurbishments (along with the closure of Rivers of America and the Train), but DLR doesn't generally announce the closures very far in advance. Being the "non-peak" season, there will probably be short(ish) operating hours on the weekdays and reduced entertainment (e.g., fireworks are
usually only presented on weekends in the non-peak season).
I think this one depends on the parade. Last week on the weekdays, it seemed like it was possible to get a front row/curb spot about 30 minutes before Soundsational and Pixar Play Parade started. PtN's curb/front row spots were gone 1 to 2 hours before the parade started, but the older daytime parades didn't seem as busy.