Place medium refiner
How and where can the medium refiner be placed? I have read about a qubic room and how can you build it? Are there any blue prints for it?

Yes, they need to be attached to a structure such as a square room or cylindrical room. You can unlock the square room early doing the base quests. The other large structure blueprints can be found on the Nexus, which you'll be visiting soon if you continue the main quest.