Applesauce as a substitution
Applesauce can substitute for either sugar or oil. Usually it is used in replacement for oil as an ingredient for keeping the item moist - banana bread, etc. It isn't a good substitute for butter since it doesn't have anything close to the same taste.

As for ratios:
1:1 as a vegetable oil substitute.

1:1 for sugar if the apple sauce is sweetened. If natural you may need to add sugar. You will need to adjust the amount of liquid down in the recipe to account for the applesauce liquid you are adding.