Do you need to mix tattoo ink with anything?

You most certainly can, and a lot of artists prefer to buy big bottles of primary colors, and then mix their own secondary colors in smaller bottles just due to the fact that it's more economical in the long run. However, it's not really advisable to consolidate all of your partial reds into one bottle though, as they will undoubtedly all be slightly different, and may give you a funky result. There isn't really an issue of sterility with this though, since they are in the sterile bottles to begin with, but still...where there's a chance of cross contamination, it's never a good idea and should not be done.