Was the term "X-Files" invented by Mulder (in-universe)? Someone else at FBI before him?
There's an episode, Travelers (S5 E15), that explains where the term came from, and it stems from before Mulder's time. It was because the "U" file drawer was too full, for "unsolved" cases, but the "X" file drawer was virtually empty.
From then on, the mysterious cases were put in the X File.
Here's the transcript of the 1990 flashback scene where the name was explained by its creator:
BAHNSEN: I already checked. They're missing but I recognize one of these names. It's in an X-file.
DALES: An "X-file"?
BAHNSEN: Yes, unsolved cases. I file them under "x." (Goes to file cabinet..)
DALES: Why don't you file them under "u" for "unsolved"?
BAHNSEN: That's what I did until I ran out of room. Plenty of room in the "X"s.