Can a faulty Water Pump [2001 Subaru Outback] cause irregular performance of the cabin heating system?

Our 2001 Subaru Outback: can a faulty water pump cause the cabin heating system to run irregularly?  
There is little rhyme or reason to when it is blows warm air versus cool air.  We smell gasoline odor
within the cabin on extremely cold days.  The odor is so strong, I will open the windows in sub zero
temperatures.  Apparently, while the engine is still cold, in sub- zero temperatures [such as 10
degrees] there is oil & antifreeze dripping onto the exhaust from the water pump.  I assume this might
be creating a low pressure condition within the water pump, which makes it difficult to heat the cabin
air?  

There was a recall for faulty fuel lines on a 2002 model of Subaru, but not for this one.

Also, we have an engine temperature gauge which ranges from medium temperature to the highest
reading possible.  Then later… it will be back to a normal reading.  Driving it fast does not seem to
necessarily make this gauge go up.  I cannot find much rhyme or reason for this symptom either.