.. What do I do with the items in the drawer?

You can't take the plaque with the cat on it, but you'll need it later, so take a photo of it with your cell phone.

As for the pages, pick them up and read them; they're in your inventory under the name "Journal" along with the page you found in the upper room.

The page after December 23, the one with the lines about birds, is going to be very helpful when it's time to solve --

-- the puzzle with the bird tiles in the ceiling of this room.

How do I solve the bird tile puzzle in the ceiling?