Can you play three skips then a reverse?
Yes, in a 2 player game, playing a skip would make it your turn again, so you could play another skip if you have one. 

Playing a reverse will also skip your opponent’s turn, only in a 2 player game.

From the rules:


  Rules for Two Players - The following special rules apply to two-player UNO:
  
  
    
    Playing a Reverse card works like playing a Skip card. By playing the Reverse card, you may immediately play another card. 
    By playing a Skip card, you may immediately play another card.