Carlsen has a 2 game lead over
Anand and there are only 4 games left. At the strength of these players, can
Magnus basically force his opponent into draws by playing certain openings or styles? Can he force
Anand into drawing the rest of the games to win the world championship?
It depends what you mean by "basically". He cannot actually force a draw in any given game (otherwise he would have started doing it already, as soon as he won one game). However he can play drawish lines; the variation he went into in game 8, for example, is almost never lost by White at top levels.
It's going to be difficult for Carlsen to "force" a draw if Anand plays something sharp like the Dutch or Pirc. His optimal strategy is still pretty much to just continue to play good chess.
Well, Carlsen certainly is going to be pretty comfortable for the rest of the games as white. He can choose lines that have a high drawing percentage.
I would expect Anand to start choosing more tactical lines as white and black. So far we've seen quite a bit of king pawn games, more specifically the Ruy Lopez. I wouldn't be surprised to see Anand break out a Sicilian or two in the coming games.