No.  The A/C is powered by the traction battery.

That, I do not know.

if you want more specific local information, I'd suggest:
http://autos.groups.yahoo.com/group/Canada-Prius/

Which Prius are you asking about?  The NHW11 (2001-2003 "Classic"
sedan) or the NHW20 (2004-current hatchback)?

On the NHW11, the AC compressor is directly powered by a belt off of
the gasoline engine.  For the AC compressor to run, the gasoline
engine will also run.  (So, in the heat of summer, the engine may come
on more often than otherwise just to power the AC compressor.)
However, unless you have the front windshield defroster/defogger
position selected or the MAX AC button pressed, the AC compressor does
not run full-time/constantly (the ICE always on).  The AC compressor
may be used if you have the AC button on, but not always.  If at a
stoplight, for example, and the cabin is already at/near the desired
cool temperature, the ICE will still shut down, and the fans will
continue to blow the remaining cold air into the cabin.  When the air
being blown into the cabin or the cabin itself gets too warm, the ICE
may turn on (even while the car is stopped/idle) just to power the AC
compressor.  The AC compressor/ICE will cycle on/off as needed to
maintain the coolness of the cabin.

On the NHW20, the AC compressor is electrically driven by power from
the hybrid traction battery.  So, the gasoline engine is not required
to power the AC compressor.  However, should the charge of the hybrid
traction battery become too low (say from a long time stopped while
the AC is on), the gasoline engine will be restarted just to recharge
the battery.  But the ICE use is independent of the AC.

Depending on your country and region, your Prius may have some small
PTC (electric) heaters to help with some cabin pre-heat (though it is
barely noticable).  However, all of your cabin heat comes from the
conventional source - "waste" heat generated by the gasoline engine
and stored in the engine coolant.  The Prius' engine is rather
efficient, as it only runs as necessary, so there isn't a whole lot of
waste heat, so the ICE may come on every so often just to provide heat
for the passenger compartment (and also to warm itself and emissions
components up).  Again, it shouldn't be constantly on, once the car
and the cabin are up to the set temperatures, but should cycle on and
off.  (There's some residual heat left once the engine shuts down at a
light or such, so the fans keep circulating this heat, but once it
gets too cold again, the engine will come back on to provide more
heat.)

No.  Just like your home air conditioner, the compressor runs off of
electricity.

Decoupling systems like this from the ICE is part of what makes a hybrid
so attractive.  There are many little items like this that can add up to
a significantly more efficient car.

In the current generation, the only heat source is the ICE.  I've been
wondering if maybe future generations wouldn't see electric-based
auxiliary heat.