Sometimes the football is placed right in the centre, sometimes it is placed to the left or right of the goal. Is there a rule for this, or is it placed where the kicker wants it to be?
Depends on where the ball was placed after the last down before the field goal attempt. If the play had ended outside the hashes on either side, then the ball will be placed on the hash on that side. If the play ends between the hashes, then the ball will be placed (and kicked) where it was spotted. That’s why a team will run the ball to the middle of the field to “center” the kick on the play before a field goal attempt.
Oh, and extra point attempts are always kicked from the center of the field.
I believe on extra points (at some levels of play in any case) that the ball can be spotted any place between the two hash marks. The center of the field is usually chosen when a kick is attempted, but a team going for two points will often spot it off center to have a longer side of the field.