Do I need both Acrobat Reader DC & Acrobat Pro DC installed?

In theory, one can have simultaneous installations of both Reader and Acrobat. However, it does raise complications as to which of the applications actually opens PDF files when double-clicking (although there is a Preferences control for that).

Acrobat has a proper superset of Reader features. Thus for normal users, there is no good reason to have Reader installed if you have Acrobat installed. And you certainly don't and shouldn't mix and match Acrobat versions. That is really looking for trouble.

The only good excuse I heard over the years was that of some authors using Acrobat that they were concerned that they really didn't know how well their PDF files would work in an environment restricted to Reader-only, especially when using forms and/or sophisticated JavaScript. However, for such testing, generally you would want a dedicated system with minimally-installed fonts and other services. Typically, a dedicated dumb system VM (virtual machine) with Reader installed would be a much better vehicle for such testing.

          - Dov