Out of curiosity and due to lack of experience with games on Linux - are all commercial games available on Linux open source? If yes, does the community review them before playing them? If not, does the community not buy and play them?
Most games aren't open because they have a specific need - they need to monetize on purchases. If the game would be completely open source, one could get it for free legally without need to pay. Other open source commercial projects use different business models to cover costs (like support licensing for example and so on). With games this is not really possible. Ideally, games can make the source open, while artistic parts (models, graphics, music etc.) closed, thus preserving the trust, while keeping the selling of final product to be theirs exclusively. Some games already do that by using open source engines, but they are still a minority. So ideally, yes. Any closed game you install is somewhat of a question trust wise. One can use Linux containers to isolate it from the rest of the system.
In case of installer or update client the situation in different. On one hand it's targeted for modifying the system, so concern is even higher than with the game itself, on the other hand GOG doesn't even monetize anything on it, so there is no reason to keep it closed at all. For the reference, Desura's update client is open source: https://github.com/lodle/Desurium
Yes but please let the operational word be OPTIONAL - I have a speedy internet connection, am not impatient and have no download caps - translation...
I would imagine it should remain optional, like Desura allows you to download a full latest package, or to use their client to update the installation made through the client. GOG will have to do the same thing to preserve the DRM-free nature of the service. I'd imagine that updates can be provided as some incremental packages as well, to avoid redownloading the whole thing again for your DRM-free backup. You can just download the original release and any incremental update package and back them up.