I am really sensitive about how much memory I have on my SSD, so I installed Galaxy on my HDD, but I play the Witcher 3 so much that I decided to install it on my new SSD.

Is it possible that having Galaxy running on the HDD will affect my performance and load times in the Witcher on my SSD? Serious question though, does it matter at all where Galaxy is installed?

You should be able to choose where your games are installed, even if the galaxy client is installed on another HDD. I don't have galaxy on this pc yet so I can't tell you how to at the moment.

Galaxy is just an interface- you don't even need it installed at all if you don't want to. You can manually download and install a game wherever you want, all Galaxy does is launch the game, and if you don't want it to, you don't even need it to do that.

It's not like Steam where the vast majority of games require Steam to be running to play, and will close out if you exit Steam.

To manually download an installer, go to a game's extras, and download the "Game Backup Copy", which will be the installer file. Install it wherever you want, then have fun- though I don't know if Galaxy will recognize the installation when you do it that way.

EDIT: After you install a game manually, you can go into galaxy and use the "Scan and Import Folders" function to get the rest back in there.

If I keep my current installation where it is, can I uninstall Galaxy, reinstall it on the SSD, and then scan for the game?

Will I still get acheivments for the game? Will it know?

No idea about acheivements as I don't have the game, but you shouldn't have to uninstall galaxy. Just manual download/install. Then perhaps point galaxy to where witcher 3 is installed.