Am I the only one missing the "Network" tab in the settings screen?
I should have this: http://i47.tinypic.com/2yxekg0.jpg
Instead I have this: http://screenshot.xfire.com/s/97793547-4.jpg

For Two Worlds 2 you can find the key in your collection after clicking on the image of the game. The key appears below the download links.

But for the first one, I just dont know. If it is nowhere, just contact the support (I have read that for some cases the key will be delivered only after contacting the support).

Unfortunately, contacting support is in fact the only way to get a key for the first game. But, I can confirm that it does work. There's a special option on the support page to request a key. It arrives within a few business days by email.

It depends on when the game was added to GOG. Early GOG releases (like Two Worlds) don't list a key, so you have to contact support whereas games added more recently (like Two Worlds II) have the key(s) listed right there on the My Games page. The earlier games have not been migrated to the newer system so still need manual requests.

There are also some games on GOG that don't need a key to access multiplayer (e.g. Deus Ex) so those games won't show a key either way.