Can I reuse the existing cement backer board when replacing tile in a shower?
Assuming that it hasn't been flexed or otherwise damaged so much that its rigidity is compromised, sure. I also assume that either you have as water barrier behind or are relying on a good tile job for moisture management. The cement board isn't usually a substantial part of the moisture envelope.

I'd use the same thinset mortar you plan on using for your tile to skim the surface. (or, if you're using mastic, get some thinset mortar).