Bless you for given Jack a home.
I just rescued a 4yr maltese with problems like Jack but her eyes are ok.
I took her to the vet and she will be getting her teeth done and pulled: spayed and toenails fixed on the 10th.
Mean while I have been feeding her sm. amount of puppy food for weight gain and using an oatmeal shampoo to help her skin and hair grow back. Also a vitamin once a day. I am walking her to help with regaining her muscle mass. Everything is working out well and she is looking great and healthy for her surgery
I hope this helps.