Is it possible to have a room protected from outside GSM microwave radiation?
All you need is a Faraday cage, with the proper size holes.

The Global System for Mobile communication (GSM) operates at 2100, 1900, 1800, 900, 850, or less commonly 450 or 400MHz.

The diameter of the openings in a Faraday cage, should be 1/10th the wavelength of the wave you want to block.

Wavelength (λ) is equal to the speed of travel, divided by the frequency of the wave.

Electromagnetic radiation travels at the speed of light (c).

So the formula would be.

Diameter mesh size (mm) = (c / f) * 10,000

So to block a 2100MHz GSM signal, you'll need a Faraday cage with ~1/2" (12.7 mm) diameter openings.

D = (299,792,458 m/s / 2100 MHz ) * 10,000
D = 14.2758313333 mm

As you've mentioned, you'll have to integrate the mesh into the windows and doors of the room. 

This colander worn as a hat, should effectively block GSM signals from melting your brain.