A kick that follows a foul?

Answer 1

In the NFL, the team receiving a punt has the opportunity to kick a field goal on the play immediately after a fair catch, even if there is no time remaining on the clock.

The team attempting the free kick must either drop kick the ball or have a player holding the ball like on a 'regular' field goal attempt. A kicking tee is not allowed. The defensive team must be positioned a minimum of 10 yards from the line of scrimmage at the time of the kick. If the kicked ball goes through the uprights, it is considered a field goal and three points are awarded to the kicking team. If the attempt is no good, the defensive team is awarded the ball at the spot of the kick unless the defensive team attempts to return the kick.

The free kick after fair catch play is rarely seen and is always done at the end of a half.

There is no free kick after fair catch rule in college ball.

Answer 2

It is called an indirect or direct kick (depending on the foul), but if the foul is in the 18 yard box then it is a penalty kick.

Answer 3

In the NFL yes.