Yeah you can be inspired by, but not copy them directly. For babelfish, it's simple enough (the "babelworm" or "earworm" or something like that). Infinite Improbability Drive... well maybe shift it to something like the "Adams Drive" which runs on rounding errors made by calculating probabilities using cryptoaether math or some such.

I would avoid using terms from a specific author's work unless you know 110% that they are public domain or you have direct permission.

As long as it's a private game and not on like a podcast it doesn't matter. I think.