You can certainly make multiple prints from developed negatives — in fact, that's why the photo lab gave you those negatives in the first place. It's also worth nothing that especially with black and white, decisions made as part of the printing process can have a major effect on the result — in today's digital parallel universe, the negative is sort of like a RAW file, and can be very flexibly made into many different expressions as a JPEG file print. (Ha! I've never had an excuse to use that analogy in reverse before!)

In the pre-digital age, making multiple prints from the same negative was the standard way to duplicate things. (You can make a duplicate by photographing a print, but that's a very lossy process.) It's remotely possible that a print lab might damage your film in the process, but it's highly unlikely.

Scanning your film will also not hurt it. (The scanner's light is not nearly bright or long-lasting enough to cause meaningful degradation.)