I have to say that the symptoms you are describing seems like "old dog disease". The thinning of the fur, the small tumors on the skin, aggressiveness toward the other dog, frequent urination and shaking. Are the tumors pink and kind of "bubblish"? Those usually occur in older dogs and are benign. They can be removed by a groomer in some cases.
Frequent urination can come with old age and the predozone. Right now I would say it's a combo of BOTH. The hair thinning often occurs on short haired dogs as they age. Especially after the age of 12. Kind of like human's hair thin out too at that age. (84)
Cushings would have been diagnosed at a younger age if it was the disease. Atleast by the age of 10 the symptoms would have been prominent enough for the vet to test for it.
Please stop doing the "internet" research on every symptom. It's just going to make you "overreact" to each new symptom. Your already taking the dog to the vet who is a professional. Let them make the diagnoses.
Your dog is getting older. They may be losing some hearing or eyesight. Keep an eye on cataracts forming. The dog's reaction to the other dog may be a reflection of this. They have less of their normal senses and other dogs can sense this. Your dog is just trying to maintain it's dominance or place in the pack. Hence the aggressiveness. Just understand your dog is getting older and is going to go through changes.