Heater not working but engine overheating

I have a 2001 Nissan Pathfinder with a cooling system problem.  This has
been going on for a couple of years now.  

It works fine for the summer – but when November comes the heater
becomes intermittent – while it is on high *( 85 ) the air comes out warm,
then cold, then warm again, then cold --- but never hot.   This may be
caused by several things;

Weak water pump
Plugged heater coil
Faulty switch
Air Pocket

However, after a time the engine then starts to overheat – The radiator  is
not leaking but it pushes water ( antifreeze) out through the overflow
reservoir until it is low on fluid – and then it overheads.   I stop and let the
engine cool down, and refill the radiator and reservoir with water – then it
will work again for a few days – including warmer temperatures at the
heater.  Then after a few days this cycle starts again.  It seems that there is
a bubble of trapped air somewhere at the top of the engine that prevents
water from circulating through the heater coil and eventually expands and
forces fluid out of the radiator cap and into the reservoir, where it gets
pushed out to the ground, eventually causing low fluid and overheating.  


Could the problem be as simple as a faulty radiator cap?

Is there a procedure for filling with antifreeze to eliminate trapped air in the
system?