My experience. I adopted a 2 year old american pit bull terrier 7 years ago. She had been owned by a guy that owned a smoke shop and was busted for drugs. She had been through 5 foster homes and no one could handle her. She was an animal killer amongst other problems she had. I lived in a one bedroom apartment with four cats, and she definately wanted to (and would have, given opportunity) kill my cats. I was determined. My cats are very dog friendly and one is very very stupid and does not understand that any one could cause harm. He will not move out of a dogs way. Sweetie (she came with the name) spent the first month muzzled, on leash with a pinch collar and tethered to me at ALL times. She slept in the bedroom with us so she got a good 6-8 hours free everyday but otherwise was on a four foot leash. Her kennel was placed in the livingroom and at first I had to cover it with blankets. I made no effort to keep the cats separated from the dog, aside from night time in the bedroom. She responds very well to a squirt bottle (she is terrified of it for whatever reason) and we used it similar to one would use an e collar. She perks her ears at a cat and tenses, she got a squirt in the bum. By the time she looked back at me I would try my best to have hidden the squirt bottle. Once she relaxed she would be praised.
I had my hands full with her as she had many other issues than killing animals so she received a LOT of training, excercise, structure, stimulation and socialization. It was about a month before I could have her in the house without a muzzle, then she progressed to dragging the leash, then eventually no leash but always kept the squirt bottle present. It would stop her in her tracks but I had to step in right away to redirect her or she would go right back at them. I structured her time out with the cats in a way that she did not have a chance to get them into her mouth before I could correct her. If I had not have been so diligent I would be minus a few cats by now. Onceshe got ahold of one of their tails, I don't know how she didn't break it. She had the tip of it with her front teeth and it took me a minute or two to choke her off until she let go.
It took about a year before I could trust her with them and relax with her out with them, no muzzle or lead. I kept a squirt bottle around though for probably 2 years. She is now awesome with the cats and accepts any new cats that come into the house. Cats outside are fair game and I am fine with that (in fact I think every gsd I own would kill stray cats given opportunity, but they understand cats in the house are pack members and respect that) but she is not to lunge or act aggressively. She sleeps with them, they groom her, they sit on her, everyone gets along wonderfully. And she also lives with 3 other dogs
I do not however leave her unattended with the cats. If I am not home, she is put in the bedroom. Prey instinct could spike at any time and I would hate myself if she killed one of my cats.
I would keep your hopes up for your dog. 7 months old is quite young still and considering Berlin has picked up a cat and not damaged it and you can do focus training around the cats, I would say these are very hopeful signs. I believe it is how dedicated you are to turning the dog around, and it sounds as if you are dedicated
If a 2 year old, out of control, owned by a drug dealer pit bull can be retrained I would think a busy, pushy, rotten gsd puppy can too
Sweetie sends thoughts and strength your way.