Arduino and Display in different rooms, possible?
Well your question doesn't really have anything to do with the arduino and the display being in different rooms. The part you linked to has an SPI interface so you will need to use the SCK, MOSI, MISO and a CS line. See here for an explanation of using the Arduino's SPI hardware.

As for having the two in separate rooms, the naive approach is to just make the wires for the above described connections really long. This may or may not work depending on several things including clock speed, line impedance, environmental interference, etc. I am not an expert in this area but these guys are.