3) I think bar from brr is actually an adjective meaning "clean" or
"pure." So it would be something more like "that which is pure." It is
attested a few times in Proverbs.
4) bar is not a construct of ben, although in Aramaic bar is the
singular of benin. The construct singular in Hebrew is ben (or bin) and
in Aramaic is bar. bar used in bar mitzvah is from Aramaic.