My DD at 2 did NOT want to meet with characters at all. Just warning you.
We have never waited in lines to meet them; if we see they are free and want to take a photo, we do, but it's not a priority.
A 2 or 3 year old can do almost anything at Disney! My DD was 2 when she rode Goofy's Barnstormer, and she loved it! She was a tiny thing, too, and we rode in front. It was very cool.
My kids loved Epcot so much. It does offer a lot of space to run, and we'd bring glow sticks for them for the evenings (it gave us peace of mind so if they were a couple feet away we could spot them). I also would hang a couple on the stroller. They loved the countries, and the snacks, and if we got into Innoventions we could never leave it seemed.
Honestly, the kids will have a great time with what you enjoy. Mine also had so much fun all day at DAK, so we just enjoyed the animals and all.
We never went back for nap time. My kids would nap in the stroller. I always brought our double Peg Perego (which had both front and back to recline, very fully, with nice cushioning). We don't usually stay up late with them on vacation, though, so we get up early and go out, then get in early for a bath and down time (to kind of decompress, and process all the input from the day).
From our first visit, my kids favorite park has always been Epcot. I can still remember my son at 4 begging for one more trip up into Spaceship Earth (we were at the BWV, so my DH got my DD ready for bed and I strolled DS over to go on one more time. So cute - he was so happy and fell asleep on the way back "home").
Definitely - do not miss Buzz Lightyear! Or Winnie the Pooh. So cute... They love those.