I have some prints of old pictures and they are all in a very bad shape.
This is an example of how they look like.
Can they be salvaged and brought to a minimally normal shape by Photoshop or by some other tool?
It can be restored. I used to be a graphic designer 10+ years ago and would have been capable of restoring it, although it would have been a slow process. People who specialize in this kind of work can do it much faster (and better).
yes it can be restored.
They can use the clone tool to clone areas of texture and light/darkness to get rid of the horizontal lines. or if your not worried about detail, using the blur filters.
If you have the negatives I could gladly help you out in doing some fresh prints.
How many prints are we talking about? Are they actual prints on photographic paper, or are they halftone reproductions in a magazine/book/newspaper? That is a big one, because if they are printed reproductions, they will likely need to be descreened, and probably lack a lot of the real resolution needed to restore them properly. I'm assuming this is a low res scan?
Just looking at the image above, there seems to be lots of detail and the damage seems quite repairable.
if you have a Costco nearby, they have photo repair service and you might experiment with one or two of your prints.