Whoa! Lots of replies. From reading all of them, I can't see a
concensus. However, I've amassed all the information and have
concluded the following:

In my first question, I believe the airplane is indeed weathervaning
during the left bank to counter the left crosswind. At the moment the
airplane is banked to the left, it is slipping. The relative wind
momentarily comes from the left, and thus the airplane weathervanes to
the left to align with the relative wind. Hence, right rudder is used
to keep the nose in line with the runway.

Regarding my second question, I can understand the variety of answers.
I believe I used the terminology "all of a sudden, a left crosswind
starts blowing". I guess it's a rather improbable scenario. From
what I gather, if the crosswind comes in the form of a sudden *gust*,
then, the relative wind would be somehow vectorially changed to now
include a slight slip component. Thus, a small weathervaning effect
to the left would be noticed in addition to the physical rightward
crosswind drift.

However, if the left crosswind comes *gradually* (in a perfect world),
I presume the airplane would only drift rightward with no directional
change.

Am I way off base here?

Thanks for your replies,
Alex (who just finished typing up his NASA form)