Maarten D. de Jong
Player A has no camels. Player B moves the supervisor and tries to send one of A's cubes to the caravan. Player A wants to play his "3 free camels" card, but it's not his turn. May he?
No. Cards can only be played on your own turn. This is answered in the FAQ, too.
Player C is about to roll the dice. Is it his turn? If so, may he play "3 free gold" in order to fund a purchase of yellow dice?
Player D is about to pick up dice for camels, but notices that if they first play "build without camels" they can construct the paddock and then when they pick up the dice have an extra camel.
He can't, because building buildings is only allowed after you've chosen a group of dice and executed the associated action. And then you can only build one building, no matter how many appropriate cards you have in your hand.
Note that when you are selecting dice, you can only play cards 'orange side up'. Granted, anything else would not be influenced by the cards at your disposal, but it makes a clear distinction between front and back of the card which aids during play.