How can i book one night at Fu Gui Hong Farmhouse?

Tedy, I just find the phone numbers. You may try to make a call to figure out whether you can book a room.
Phone number: +86-10-60681116 or +86-13716176393.

How far is the Fu Gui Hong Farmhouse from the entrance to the Wall? Is the entrance near the cable car?

Tedy, the farm house is a bit far from the wall, around 13 kilometers. You can walk to Xisancun (西三村) station to take H24 to get off at Mutianyu Roundabout. The new ticket office is very close to the roundabout. You need walk to the ticket office to buy the tickets and take shuttle bus to reach the original entrance. It's about 3 kilometers from the new ticket office to the original entrance of the wall.

Thee original entrance is also called South Entrance. The cable car terminal is a bit far from the south entrance, but very close to the North Entrance.