I've just downloaded GOG Galaxy and was wondering if I install games from my library will any of my progress from the games I have installed on my computer be carried over to GOG galaxy or not. (P.S. any other ins and outs I should know about GOG galaxy that would be helpful or useful or cool?)

Are you asking about GOG games that you already have installed? If so, then adding the game to Galaxy won't affect your progress. It simply adds the game to Galaxy and you can launch it from there if you want. You may get the benefit of cloud saves and time tracking, maybe even achievements if the game in question has Galaxy integration to support those features.

Yeah, you should be able to import them just fine.

Yep, client knows everything about you...

Then why didn't it give me a birthday present?

It's not there for Your benefit...

So if I install the games to Galaxy, my Morriwind game where I am in Vivec for the main quest will still have my saves if I install and open Morrowind in Galaxy?

If you have GOG version of Morrowind installed on your computer, then you don't need to install it second time through Galaxy. More likely Galaxy will notice that you already have this game installed and add it to the list. You may need to verify files if Galaxy will show something like "Unknown version". This will not affect your saved games.

If you have non-GOG version of Morrowind installed (CD-version, steam version, etc.), then you will need to install Morrowind through Galaxy. This will create the second copy of the game on your computer. Those copies will share saved games. This is not really good to have two similar programs at one time as you will need additional disc space. You may install Galaxy Morrowind in the same folder but this may create difficulties for future uninstall. So if you already have Morrowind installed, it is not GOG Morrowind and you want Morrowind in Galaxy, the best way is to backup your saved games (never trust an installer to keep something important), uninstall your existing copy (selecting to keep saved games), install the game from GOG installer (offline or Galaxy). If the installer works correct then you will have your saved games available (in the documents folder). If something gone wrong use the backup to restore your saved games.

Simply use GOG logo located in top-left corner, Scan and Import folders and head to the folder with installed games.
In case any trouble, open the game page (i.e. Morrowind), click more button (next to play/install) - > Manage installation - > Import folder.. (or Verify/repair, if the game was already imported).

Your saves are safe ; )