ubiquity (n.) [...] + que "any, also, and, ever," as a suffix giving universal meaning to the word it is attached to, from PIE root * kwe "and."
I looked it up in Pons online Latin-German. There are so many translations of -que there, including some in which and simply doesn't work at all as a substitute, that any dictionary that presents and as the only translation must be considered incomplete.
Also is essentially a synonym of and when connecting two sentences. Since -que can be used in this way, it is not at all surprising that also made it on the list.
Fdb has explained where the translation -ever comes from. This explanation could also justify any-, since ubique can also be translated as anywhere. There may well be a better separate explanation for that, but I haven't found one.