If dessert has to be cooked on site, we have had luck with an upside down cake cooked in a cast iron pan. Won first in dessert once with an upside down apple cake and twice with upside down pineapple cake. A cheesecake does pretty well too - got a first place last year with that. I think the trick is to cook without using any wood, just charcoal.
For chicken I agree with GrillsGoneWild. Basically do a spatchcock chicken split down the middle.