Do I have to install the game to know whether or not I successfully purchased the Flashpoint expansion? I don't see it in my library, either on its own or in the Battletech window. Don't see any serial keys under More either.

You should be able to see a Flashpoint DLC installer under the BATTLETECH entry in your games library (I'm looking at the backup downloaders, not the Galaxy stuff, not sure if matters).

That said, I can't get it to actually install, so having purchased it is, shall we say, small comfort.

Supposedly in the Main Menu it should say "Installed" instead of "Available" after Flashpoint in the top left corner.

Not working for me, though, just tried it after reinstalling.

You can try "Settings". THere should be a list of the DLC there. Clicking on the empty square should make the trick.

On the first day, the name was a numerical code. Today it appears with its proper name, "Flashpoint".