DH and I spent all day this past NYE at Epcot, starting with early entry and leaving the parking lot at 1:30 am!! It was crowded, but fun. Like others have said, be sure to make PSs for your meals.
We figured AK wouldn't be too crowded, since it was the only park not open till midnight, but the CMs told us it closed to capacity before noon! It also closed another day earlier in the week due to capacity.
From what I have heard, MK is pretty empty early on NY Day, but later it gets full as it normally is still open late and Spectro is still running.
As for dinner NYE, it might be easiest to meet and eat outside a park, like the Boardwalk area or a resort restaurant. If they aren't worried about getting back into a park later, that's your best bet. If they want to be in a park, you'll have to hope it's still open for guests to get in for the PS. Keep in mind there are levels of closure. Parking lots close first, then they close to offsite guests (those not staying at a WDW resort), and finally all guests. All on-site guests are guaranteed entrance to "a" park on NYE, but not necessarily the one of their choice.