firstly- i purchased the game yesterday from the gog.com site via credit card purchase and it hasn't yet shown up in my library. do i need to wait a couple of days for the transaction to be processed?

secondly- do you need to have galaxy installed to play it or can you just run it from the gog site?

First, Hearts of Stone is a DLC, so it does not show on your library separate from The Witcher 3. It is part of The Witcher 3, so that's where you'll find it.

Second, no you do not need Galaxy to run it. Just download the installer from your account and install it manually. Run it from the shortcut it creates on your desktop.

ok thanks for that :)