May the kick-off be taken by a person other than one of the players taking part in the match?

No. If, in certain matches (e.g. charity or exhibition matches) a ceremony is arranged for a person not taking part in the game to kick the ball, it must be brought back to the centre of the field and kicked off in accordance with the Laws of the Game.

When extra time is played, which team kicks off?

A coin is tossed and the team which wins the toss decides which goal it will attack in the first half of the extra-time. The other team takes the kick-off.

If the ball is kicked straight into the opponents' goal from the kick-off, what decision does the referee give?

A goal.

What action does the referee take if, at kick-off the ball is not played forward?

The kick-off is retaken.