You could try scanning with a lower dpi (dots per inch).
I found that when scanning at a higher dpi you pick up every scratch, particle of dust etc.....then you end up spending a whale of a time touching up.
I use Corel Paint Shop Pro to do my finishing of my photos and it has many correction that might help you get a better photo.
I would imagine that Photo Shop or any progran could give you the same abilities to correct.
I found that "pearl finish" was a pain.
As for your other question about stains and fungi....scan the photo and use the "cloning tool" to clear up the problem....I would be leary of trying to clean the original photo, as you make take off the emulsion....but then, what do I know.