Wind direction measuring circuit
No.  A dead spot means there is effectively a large resistance in series with the wiper, not that it shorts to anything.

C1 is to filter out some of the high frequencies that are clearly not part of a valid signal.  Even in a hurricane, there is some rather low (relative to what even simple and cheap electronics can handle) maximum signal frequency on the pickup coil.  C1 probably just shorts out things like radio station pickup.

D6 and D7 are clamps.  They should never conduct in normal operation.  They are there to protect things in case of a screwup or failure elsewhere that could put too much voltage on the pot.

It seems from your description it is only on one side.  Measuring it would tell you for sure, of course.

Your quote is out of context, so this is hard to answer.  In general, expect spikes and other noise to be present on external signals that come in from off-board.  This seems to be just telling you to use normal precautions for external signals, like make sure your device doesn't blow up if one of the signals is accidentally connected to the power line, or gets zapped by a static charge.