You can't take a pawn en passant if that pawn just made a discovered check to your King:
After 1. d4+ Black is in check (their king is attacked by the White bishop on c1) so he has to move his King. 1...cxd3 is not allowed.
Also, it can't be carried out if your pawn is pinned to your king:
The Black pawn on c4 is pinned by the White Bishop on a2. If that Pawn moves, the White Bishop would be able to take the Black King. So after 1. d4 the move 1...cxd3 is not allowed.
I can't think of any other condition where this move can not be carried out.
And yes, en passant is allowed in tournaments of course. But when you take a pawn en passant, do not say "en passant" aloud (some low rated players do that, they also say "check" aloud when they put the other player's king in check) since it can break your opponent's concentration (and the concentration of the other players near you in the playing hall).
For explanations about the en passant rule, see this good Wikipedia article: http://en.wikipedia.org/wiki/En_passant