In a free-for-all, can I play Actions and Reactions in a showdown that I donʼt have units at?

Yes. Starting with the player who contested control/the attack, players each get a chance to play an Action or Reaction. Other players can then react with Reactions, but once everyone passes, the next player in turn order can play their own Action or Reaction. Continue like this until all players have passed on an empty chain, and then move to the end of the showdown.

Related: Rule 345, Rule 347.1, Rule 347.2.b