.. What should I take from the display?

Look at the coins in the blue folder on the middle shelf; you can't take them now, but you will at the end of the game.

Endgame: After You Call the Scientist

There's a dragonfly-shaped bug on the boots; grab it. The perfect place for this bug is --

-- in the flowers in Zoe's room, where there are already some dragonfly ornaments. Yay! Place it, then go to the cabin to listen in.

What do I do with what I learn?

Finally, the missing cipher wheel for the cylinder puzzle in the cabin fireplace is on the left side of the middle fireplace.

How do I open the cylinder puzzle inside the fireplace safe?