A summary of the rules above is that a Communication path may start in a US controlled hex but not be drawn through such a hex after that (unless it's bocage or another German unit is there).
Correct, basically a hex in US control is eligible to receive reinforcements but its communication path must not pass through other US controlled hexes.
In your case:
-A4 is surrounded, so if you start tracing communication from this position, all successive hexes are US occupied or US controlled.... so not elegible
-A6 can receive a reinforcement, the hex itself is US controlled but the hexes above it are not, it is eligible
-A2: I cannot judge this one. The position is in US control but the hex on the right (west) is not. Communication path may start in A2, go through the hex on the right, and from here continue down the draw (there's just one hex -1211- not US controlled here) and then proceed further west