I couldn't find any resource about this. I know that shouts have cooldown, but are they shared (as in, if Shout A have 30 secs cooldown, and I used it, I have to wait 30 seconds before I can use shout B ), or do they have separate cooldown for each shout?

They are shared. If you're on cooldown for one Shout, you're on cooldown for all shouts.

Which is unfortunate but fair as far as game mechanics go. Early on in the game I came up with a plan to take down a dragon that was wiping the floor with me involving multiple shouts and never stoppd to consider the cool down. More floor wiping commenced.

Shared. Which makes storm call kinda useless because it's hard to go 5 minutes without supportive attacks

Dang. Well, that's it I guess. I always find it a bit strange that I can't Whirlwind right after Unrelenting Force. Would've made a very great scene.