As far as treats go, popcorn and honey are always a hit.
Foods they always seem to munch are walnuts, freeze dried krill, fresh or dried greens, raw eggshell, watercress, cilantro, coconut, dried flowers and leaves, most dried fruits, chicken livers, and deer meat.
As for when to remove foods, it depends on the food. Things that get really stinky and gross quickly (like say eggs or seafood) I remove the next morning. Things that hold out a little longer, I leave for another day or two. Pretty much I change it out whenever it looks gross.