I think they are open until 8pm (but don't quote me on that). When we were in Epcot last September I remember having to rush around to finish them all in time (we started late). I hope this helps.
On our visit in Mar '02, they didn't open until 1:00, but someone posted that they were opening at 11:00 now. I hope that's still true next March! I'm not sure about the closing hours.
I had promised myself I wouldn't even try to have my 3 and 5 yr old at any of the parks after 8, but it looks like there's so much at WS that I just might have to bend that rule We'll just play it by ear.
We were there July 5-12th and my kids did KidCots and received their stamps until 9:00 p.m. We weren't doing illuminations that night and they finished up their passports and masks after we finished supper at about 7:45. I'm guessing they stay open later during "peak" times.