Chromaggus and fatigue
Solution 1:
No, Chromaggus does not cause you to take any extra fatigue damage. The wording of the card is "Whenever you draw a card, put another copy into your hand." It doesn't add extra card draws, it only duplicates the card after it is drawn.
In the official BRM reveal stream, they go into fatigue with Chromaggus on the board and only take a single fatigue hit.
Skip to minute 54 to see the play in question. http://www.twitch.tv/playhearthstone/c/6438751