I haven't been in April so don't have any personal experience but my guess is that it will be very busy but you can still get a lot done during the first 2-3 hours in the morning if you are there when the park opens, including hitting some of the major rides. Basically, get to the park about 30 minutes before it opens (usually 9 a.m.) and then head over to one of the major attractions that you want to ride (Soarin', Test Track or Frozen) and then go ride the secondary rides with minimal wait. There aren't a ton of rides at Epcot (unlike say Magic Kingdom) so in 3 days you should be able to ride all the rides you want if you get there early. You definitely should take advantage of Fastpass as well. So rides in the morning, maybe head back to your resort around lunchtime to hang out at the pool, then back to Epcot in the afternoon with dinner reservations in the park and to walk around and enjoy the food booths.
I just did some spot checking and there are plenty of reservations available around 1:00 each day for the table service restaurants in Epcot. The evening availability is more limited but there are still a lot available. For example, you can book Chefs de France, San Angel Inn or Teppan Edo for lunch dinner on April 22 or 23. Those are probably our favorite restaurants at Epcot. You can also walk out the back gate of Epcot over to the Boardwalk area and there are a number of restaurants there. You should make reservations now -- you can always cancel later, but make sure you do so if you don't intend to go because you card will be charged if you don't cancel and are a no-show (you have to use a card to hold reservations, though no charge is applied). And if you do the dining plan, you can use your snack credits at the food booths.