Chelsea should win the game. Fulham have played well as they beat Arsenal 2-1 on new years eve but Chelsea have won back to back Premier League games and there is a strong case for Chelsea to take all three points. As for the other game you mentioned, Tottenham will probably win the game. Even after Manchester United beat Aston Villa from 0-2 down to win 3-2, I am expecting them to return to their real form.
West London Derby with Chelsea vs Fulham... That game will be played with much tenacity and I wouldn't be surprised if they win the match seeing that momentum is at their side.
Man United vs Tottenham, I think a lot of people would side with Tottenham here as United have been terrible this season. But I'd say just stay away as United in the Theatre of Dreams could disappoint they away side.