Do rules revert to 4 player rules midgame if someone gets eliminated?
No, nothing changes. The TI3 FAQ puts it fairly straightforwardly on the left hand side of page 2:


  Elimination
  
  A player who controls no planets and has no units on the board
  is eliminated from the game. He cannot play Action Cards or
  choose Strategy Cards. After a player has been eliminated, the
  other players continue the game normally, with no changes
  to the number of Strategy Cards taken, etc. When a player is
  eliminated, all his Action Cards are discarded and all of his
  race's Trade Agreements are removed from the game. 


Once a player's eliminated, everyone plays by the same rules as they have been the whole game. You don't revert to rules for the current lower number of players.