Hello,
You are not alone. So many of us have gone through some or even all of what you are experiencing. You just got a heaping helping in one swoop..
OK.
ONE thing at a time.
Skin problems take time to resolve and get cleared up. As much as a year so don't fret too much. I had one dog that had horrible skin problems and had bald patches so bad. But all of the fur grew back and you can never even tell any problems existed. IN fact, her hair is even smoother and better now than before she went through the problem. I'm sure it was and is because of the better treatment of food, shampoos, etc.
AS for the apple cider vinegar, it is one product. After you bathe your dog, mix a 50/50 of just water and vinegar and slowly pour and rub into the coat. If you pour too fast, it just runs off and you waste it. Pour slow, rub...wait... spend time talking to your dog while you wait. Rinse with cold water. Towel dry. WE start all of our dogs and puppies using a blow dryer after the bath to help dry the skin faster and the mild heat kills any surface problems. They love it as an adult now and know to go into the puppy room which is where we keep the blow dryer. They will lay on the floor and ooohhh and ahhhh while getting blow dried.
AS for the food; many good suggestions above. Start slowly. Mix over the course of a week if possible to transition or else you have another issue to deal with. The top 3 star levels all have dog foods that work with bullies. But certainly stay away from the bottom tiers, anything with chicken (meal or product) and a grain-free is better. Adding in yogurt helps to stabilize the GI. IT IS VERY IMPORTANT TO LOOK AT THE POO EVERY TIME THEY GO. You can detect and catch problems way before they blow up just by knowing if there are any changes in the poo. Gross..yes.... but if you pick up as soon as they go, you will see it fresh. Any changes in color or texture can alert you to problems. Many go away on their own, but you will know something is going on. Also, picking up ASAP prevents flys, bugs and other problems from building up.
The eye problems are rather common and 99.9% of the time work out with no problems. Don't worry about that.
And finally, as for the immune system. You can't do anything about it know, but depending on when the puppy shots were given does play an important role. The puppy has no immune system when they are born. They receive antibodies from the mom from nursing. Was the mom properly vaccinated? Was anything passed on? The puppy/mom anitbody only works till around 8 weeks. This is the cross over period when puppies are very prone to problems. This is why giving puppy shots has to start early enough to start to build up immunity for that cross over period. Take a deep breath.
Your emotions tell your dog how you feel. Be positive and happy. Use your love to help get through this. This too shall pass.
Good Day~