Its a much simpler solution. You don't have problems with file sharing and viruses, you don't have to allow a strange computer into your network (and possibly eat up bandwidth). If the files just get copied over once and the drive gets returned to you, there's little chance of breakage. You can even get the other guy to buy the drive himself and give it to you every week. If he wants you to go through the trouble of figuring this all out for his benefit, he can pay for the hardware himself.
Your solution is running Cat5E cabling on the outside of a building on the sixth story through PVC shielding. How you're going to do that without a movable crane is going to be a tricky task. I don't think you've accounted for rain getting into the pipe somehow, or attaching to the cable itself and running into your Ethernet port. I did network installations for a local ISP that uses a wireless WAN and several of our Ubiquity routers were damaged in that way because of improper shielding for the cables that ran through the holes drilled in the side of the building.
Do you have any mock-ups of a floor plan for this building you live in? If you're on the same level, is there no courtyard in the middle of the building? Do the doors of these two flats not face each other in some way?