Some of the games I bought will have an 'updated' icon next to them.

Where do I find info about what was updated?

Is there a fee to update my existing game to the updated version?

Does the gog downloader recognize the older version and install over it?

Updates are free, but the information about what's been updated isn't usually clear. There's a what just updated thread, and that's about it.

Other than the What did just update thread hedwards mentioned, there should also be a thread about the updates in the games' subforum.

I always head to the game forum when theres an "updated" tag on one of my games. The patch notes are always posted there.

I don't think the GOG Downloader is smart enough to do that yet, so you have to update your games manually. Some of them just make you apply a small patch, but some do require a full game reinstall to work.

And no, you don't have to pay anything for them ;)