From the looks of it, the Dragonborn would have trouble teaching people how to shout considering it's an inborn talent more than anything else. He/she just can, where as others learn. It would be like if he/she were trying to teach the blind the colour blue, or to put it in D&D terms a sorcerer teaching trying to teach a wizard how to use magic.
Just because someone learns something easily doesn't mean he can't teach it.
Besides it's an inborn ability for
but he can still teach it.
No, the Thu'um is only for the Dragonborn, and is also useless without having dragons around to absorb from.
If it's only for the Dragonborn than how do you explain the Greybeards.