Borrowing heavily from Cami, as we're just back from DW ourselves:
2. Kids often surprise parents with their preferences. Example: kids are often just as thrilled to go swimming than they are to go on rides. So make sure your hotel has a good pool and you bring swimsuits and PLAN for swimming (and also the need to take decompression breaks because the parks are often overstimulating for children).
YES. DD was asking to go back to the hotel after 2 hours at the parks. We took a 5 hour nap + swimming break every day, which really ate into park time but worth it to have a rested, happy kid.
3. I'd skip Epcot and possibly Hollywood Studios at Disney. We love Epcot, but with a very few exceptions, most kids are not fans of it.
Granted, we only spent about 2 hours at Epcot but DD loved the Nemo ride, which shares a building with a decent-sized aquarium and she could have spent at least another half hour staring at the fish. Definitely varies by kid tastes. We would have liked to explore more but a lot of the walk-through exhibits close at 7 pm even though the park is open until 9 pm. I think by 8, only a few of the big rides were still open (and still had 45+ min waits!) and everything outside of the International Village was shut down. If you go, go in the morning!
4. The best way to get the most done with the shortest lines is to get to the parks at "rope drop" -- which is as soon as it opens. By doing so, you will be able to get on rides while waiting the shortest possible time, which allows you to get on more rides before the kids get tired and/or the parks get crowded. If you do not get there for rope drop, plan accordingly and understand that you WILL have to wait on lines, sometimes long lines. Prepare everyone for that reality.
Painful to get up that early but totally worth it. We walked on to the most popular rides with little or no waits. The FastPass system works well too, although they do run out an hour or two before the park closes.
FYI, watch for the different park closing times - Magic Kingdom is open til 11 pm most nights, Epcot til 9 (though lots of things close earlier), and Animal Kingdom only til 6 or 7 pm. Staying at a Disney resort is supposed to mean you can take advantage of earlier mornings and later evenings at the various parks, but they were so infrequent that it never worked out for us.
Similarly check the daily schedule for the other parks. We planned to go to Universal on Friday, only to find out that it closed to the public at 6 pm for a private event (high schools rent it out, apparently). That was a real bummer.