Operation Wignut
USSDF Riot Squad
I don't know for sure, since I don't think I've ever seen a terminal in the game smashed open so you can see the components. But since all the other electronics in the game seem to pre-date transistors and integrated circuits, I'd guess they probably do use vacuum tubes.
Yes. Transistors and semiconductors were never invented/discovered in the Fallout universe.
Well, correct me if I'm wrong, but vacuum tubes wear out after like 40 years. So I don't think terminals would actually still work.