Glad to hear things are better there now...! I think I have never seen that kind of a roof... Tile? With a texture? I don't know what that is called, English isn't my first language haha.
Yeah, neutered dogs do tend to gain weight due to a lack of certain hormones (I mean, we too, as we all age). Make sure your friend has a little extra time to play fetch and walk, and perhaps consider changing her rations. There are a few formulated towards neutered dogs that have a lower amounts of carbs and fats. It helps them to keep within healthy weight range. :)
Ah... I don't know about coconut oil being good for fungi, but I have personal experience with clove oil. It works very well. And yeah, it can take awhile (like, a week) for results to show. Fungal infections are a pain to heal. Even after it looks good, make sure to keep the area clean and keep applying medication for another month or so, to make sure all the spores are really gone. It may break out again otherwise.