i don't know about the litter box door, maybe leave the top off?

some cats just don't like the cat treats. or it could be the flavor.

the soft cat food can last 2 or 3 days in the fridge. make sure you cover it with plastic wrap or something. or the whole fridge will smell like cat food.

BTW there's a community called cats, were they might be able to answer your questions better.

http://cats.dreamwidth.org/