Kohleran: If I uninstall a game, do I have to download the game again?
If not, where do I look to find the games files to install again without having to download sometimes very large files?
timppu: By default, yes uninstalling a game through the client (be it Galaxy or Steam) will remove the game files from your system, because that is what you are asking it to do.
If you want to avoid having to re-download the game whenever you want to re-install the game (be it onto that same PC, or installing the game on several PCs without having to download it on each of them), you have one or two options:
1. Like others mentioned, download the standalone backup (offline) installer files. You can download those standalone backup installer files either with your Galaxy client, or a web browser.
You can install your game using those installer files, and from what I understand, Galaxy should normally detect such manually installed GOG games as well (or, you can run those games without Galaxy as well). If Galaxy doesn't detect the game, then I presume there is some "import" option there where you can tell Galaxy to "import" the manually installed GOG game into Galaxy.
2. It MIGHT also work that you simply zip and copy away the game installation directory (that Galaxy created when you downloaded and installed the game with it), containing the installed game files. Then later when you want to "install" that game back into Galaxy, unzip that folder and import it to Galaxy?
I am just guessing with this second alternative, but in theory it might work. I can't test it because I am not using Galaxy, I play my GOG games installing them with the aforementioned standalone installers.
Yes games still work when you just copy the directory to another location. The games even work without galaxy if you start from the exe instead of the shortcut "Launch game X"
Inside galaxy you can set which directory's gog should search for their games. C:programfiles(x86)\galaxygames D:\gog E:\GoG etc all games stored in the set folders will be recognized and added to the library even if you move them