If memory serves I saw all three of these situations in college football many years ago.
Quick Kick-This is not the quarterback lining up in Shot Gun formation and punting. A Quick Kick is a punt with any runner, including the quarterback, kicking the ball at or near the line of scrimmage. It is the very opposite of a fake punt. Like anything else, working properly that ball will roll a long way.
Third Down Punt -When using this, a team must have almost no faith in its offensive unit and faces a long yardage situation.
Single Wing-Three backs are at a 45 degree angle to the offensive line. The snap goes to the Tail Back and the quarterback and wing back can run or catch the the ball. There are double tight ends. As you might expect, this formation involves a running game with very little passing. Princeton and UCLA used the single wing in the 50s but now it almost nonexistent.