I believe shouts use up Stamina, which recharges naturally like in previous games. As for the original question, I'm pretty sure most dragons will land at some point. From the videos I've seen, it also looks like they'll sometimes fly low enough to get a good strike in.
Untrue.
Shouts that use Stamina, use it because it makes sense. Whirlwind Sprint uses stamina... it makes sense... it's sprinting.
Shouts that logically don't need stamina, don't use stamina. Unrelenting Force doesn't use stamina. It's a shout (I mean literally a shout... you know.. a SHOUT shout.. like force push... but with your voice?... ok, I'll stop now)
Shouts don't use magicka either (none that I know)
Shouts can be used more than once per day.
Everytime you use a shout, a "gradient" effect appears in your compass bar. It gradually moves outward in both directions. When this effect reaches the edges of the compass bar, your shouts can be used again. The time it takes for the effects to move all the way to the edges represents the shout's recharge time.
If you hold down the Shout button when shouting, your shout will use its higher levels (level 2 and 3) instead. The higher levels have a longer recharge time.