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Just downloaded GOG Galaxy and could not be happier :-D
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To answer your question: "Where is the game manual located after you download it?"

Through GOG Galaxy client:
I'll quote mepe_ruse from another thread asking the same:

"In the Galaxy client select which extra you want to download.
At the bottom of the dark Grey box on the left hand side of Galaxy you will see a circle with an arrow pointing down inside it, when your download is completed click on this icon.
You will now see a list of your recent downloads, hover your cursor over the file you want to locate & click on the circle with an Magnifying glass inside it.

If you want to change the file your extras are downloaded to click on the Gear symbol at the bottom of the Grey box in Galaxy then in the settings windows that opens check the box "Manage all folders manually" & select where you want to save your extra downloads"

Or directly through the filebrowser:

probably smth like:
"C:\Program Files\GOG Galaxy\Games\!Downloads\"