In Haunt #43 - The Star Sickness, does any use of the serum on a traitor kill them?
Yes, the best way to determine if someone is a traitor is to (attempt to) inject them with the serum.

If they are a traitor they are killed by agreeing to the serum, and if they are not a traitor it completely absolves them of any current or future suspicion, plus heals them back to their starting values and stops them potentially taking damage each turn from the physical attack that occurs on the haunt revealer's turn (this is not directly stated, but is implied by the rules).

If they refuse, you then have a fairly good idea that they are a traitor, after which they can then do their best to infect you, or die by other means and become an alien.

As for your confusion over the serum, any explorer can use it, but it would mostly be pointless for a traitor to (the only good case I can think of for a traitor using the serum on another explorer is to redirect suspicion).

Note that on becoming an alien the explorer drops all items and that aliens cannot trade items. This seems to indicate a general intent in the rules for aliens to not be able to use items, but it also specifically says that aliens are treated as monsters only for the purposes of movement and taking damage, thus rules-as-read they are not technically prevented from later picking up or stealing items.