How old is your system? I never touch real old black iron pipes like that without first warning of the worst case scenario. That is you break a pipe or fitting, none of the fittings will come loose without breaking and the pipe is to worn or you don't have the room to thread in place. Meaning it's possible for a simple repair to turn into a re-pipe.
As for teeing off I wouldn't tap into other radiators lines. Each radiator should have it's own line coming off the main pipe.