PPI doesn't measure the connection between two regions, for that you would want to use resting state data. PPI measures how the connectivity changes with a task.
If you find that for c1, the PPI model for region A has a significant change from baseline or another task in region B, then one may or may not find that for c1, the PPI model for region B has a significant change from baseline or another task in region A. The reason for this difference is that you don't know what all the sources of activity in region B. For example, region A may increase its connectivity to region B during task c1 relative to baseline; if region B is connected to many other areas as well, then the connectivity of region B to A may not change because B doesn't match the signal from A.
As to your last point - which again should be performed with resting state data since you are looking at the connectivity between regions and not changes with task. No that is not the case. If A and B are correlated at 0.5 and A and C are correlated at 0.5. This won't tell you how well B and C are correlated.