cake undercooked or too wet?
Your cake did not rise properly because of the substitution you made. 

Oil and apple mousse are only an acceptable substitution for butter under some circumstances. When a recipe directs you to cream the butter with the sugar, you cannot use a non-solid fat substitute. The creaming creates a bubbly, airy structure, and these mini-bubbles get expanded by the baking powder. If you dump a liquid fat in, this won't happen, and your cake will stay un-aired. It will be doughy, which you perceived as a moistness. 

By the way, the sugar also plays an important structural role. I would advice you to not reduce it in cake recipes, as you will get a worse texture (although the results won't be as problematic as with the butter substitution). 

If you want to make cake that requires creaming and don't have butter, you can get decent results with shortening, margarine, lard (caution: the taste will be noticeable, will not do for fine tortes), coconut fat, and other solid fats. If you don't have any of these, you have to choose a recipe which uses a different method for combining the ingredients.