During a penalty kick, the kicker taking the kick runs up and fakes a kick which fools the goalkeeper, quickly takes the kick, and scores and scores a goal. I know that would be unsporting behavior. What’s the correct restart if no other infringement happened? IFK for the opposing team?

USSF answer (August 10, 2011):
Law 14 tells us:

Infringements and Sanctions If the referee gives the signal for a penalty kick to be taken and, before the ball is in play, one of the following occurs:

the player taking the penalty kick infringes the Laws of the Game:
* the referee allows the kick to be taken
* if the ball enters the goal, the kick is retaken
* if the ball does not enter the goal, the referee stops play and the match is restarted with an indirect free kick to the defending team, from the place where the infringement occurred

To this the Interpretation of the Laws of the Game and Guidance for Referees (back of the book) tells us, under Law 14:

Feinting at the run-up to take a penalty kick to confuse opponents is permitted as part of football. However, feinting to kick the ball once the player has completed his run-up is considered an infringement of Law 14 and an act of unsporting behavior for which the player must be cautioned.

In brief, no, an indirect free kick is incorrect. It is a retake of the penalty kick (or the kick from the penalty mark) after the referee issues the caution. And a different member of the kicking team may take the kick.