Looking at Schmalenbach's schematics, once the target was designated both the appropriate director and the appropriate rangefinder were put on target and controlled by the computer/operators. It could be any rangefinder and any director, or any radar.
Yes. The communication between director and calculating center worked as a closed circuit. The director gave initial direction with observed enemy speed and course. The calculating center did its bit to convert all data into rate of change and sent back training and artificial horizon to the director, range finders, etc through remote power control. The director crew by detecting errors in train could then make corrections which were fed back to the calculating center.