Hi, Bob. I'm very much afraid that your only recourse can be spelled out in two words - MOVE QUICKLY. I hate to be so cavalier about it, but it is obvious that serious problems exist in the wiring in this building...problems that can only be remedied by completely replacing the electrical system (a very expensive proposition when done CORRECTLY by a properly licensed professional). The building owner either doesn't care or is oblivious to the peril that you and your family face. Being on the third floor of this building only makes this situation more grave for you in the very likely event of a fire.
I don't see how on earth it would be possible for this building to pass inspection. Any electrical inspector I have seen would immediately order the electric service to be terminated until such time as the system was brought into compliance.
Best of luck to you, Bob. I guess the bottom line is...I fear for your safety.
Mike (mamills)