Wow, that's another awesome feature. When they say "you can save your games in the cloud", do they mean game data, or actual games you buy and download?

You game data can be uploaded, and it is done so automatically.  Your games and DLC are always available in the "Cloud", as with the Xbox 360.  No change there. 

Does that mean if you download a game, store it to the cloud and go to someone else's house, access to your account you get to play right away without downloading?

No.  Like the PS4, there is an initial amount of the game that needs to be downloaded before the game will start playing.  But once that happens, the rest of the game is streamed down to the console (downloaded) while you're playing.  However, if having your game accessible without redownloading it, you can save the game to a thumb drive or external HDD, and play it using your account.  Or if it's a disc-based game, take the disc over to your friend's house, insert the disc into their Xbox One, and play the game.

Cool, but I'll just be using my own media storage devices.

I would rather not put my game saves in the cloud, I'd rather have them on my console.  Also maybe its just me, but it sounds weird that you can install the game on the cloud, since all games require installation, I would think you need to install them on your console.

Is it confirmed that you can use external harddrives with the X1?

Yep via USB. 

But what if the cloud servers are down? Can you not play then? 

now this a good benefit to welcome back always online...