In my opinion, the first wasn't and the second was (contrary to the majority here).
The question is, did Villa gain an advantage? Agbonglahor was actually going away from the goal towards the corner of the box, (into a non-shooting position), at the point he was taken down. The ball was then run-onto by the attacker, creating a shooting opportunity which he missed. I would therefore conclude that an advantage was gained and therefore no penalty should have been given! However, I do feel that a penalty could have been given immediately, as there are very few instances where there is a better advantage than a penalty kick (excluding an open shot on goal etc.).
The second penalty - contact with the player before the ball - penalty kick!