Is there a risk of damaging the repository (using a file share) if we use different versions or the tools to pull from and push to the central repository?
FYI: The central repository was created with Mercurial 1.5. We are planning to upgrade our tools to Mercurial 1.8 with Tortoise 2.0.
What you're describing is safe to do. Every version of Mercurial can safely read and write repositories created by older versions. Older clients will refuse to read/write repositories that are too new for them.
So as long as you're accessing repos created with 1.5 you can do so with 1.8 just great.
More detail: https://www.mercurial-scm.org/wiki/RequiresFile