Hi Yeal,

Dr. Leela has indicated on another post, that she will take a look at your case and help you out with a prescription.

Obviously the food change is helping the dog (decreased urination). We see quite a few cats who "come down" with diabetes and other endocrine disorders from a life time of commercial food. The coat of the animal is usually the last thing to "come back" after major system disfunction.
I think the nose is probably dry like the rest of her body. Omega 3 and 6 (great source is in human grade salmon oil) may help restore her coat. Flax oil is also a good supplement. Perhaps adding a couple of teaspoons to her food every couple of days may help. Also if she allows you to brush her, you can help distribute body oils that may be collecting in areas due to poor circulation. I prefer a rubber (scaled down verson of a horse brush)for this task.
Hang tight, I'm sure Dr. Leela will post soon.