YES
According to the 2009/2010 version of the Laws of the Game as regulated by F.I.F.A., under Law 8- The Start and Restart of Play (page 27 in the official "Laws of the Game") under the heading "Kick-off" it states:
"A goal may be scored directly from the kick-off."
You may verify my answer by going to www.fifa.com and download the Laws of the Game pdf file.
Yes you totally can do that.
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Yes. A goal may be scored directly from a kick-off, but only against the opponents. See Law 8 of the FIFA Laws of the Game.
Not directly, no. Another player must touch the ball before a goal may be scored.
No, once the balls has passed over or into the plane surrounding the endzone it is deemed a touchback and the ball is placed at the 20yd line. But if it did happen that would be sweet.