My advertised involvement?

1) Does " to my chagrin" mean "to my strong embarrassment"?
2) Does " my advertised involvement" mean "my presence (of this meeting) that is advertised (by Templeton Foundation)"?
3) Does "its legitimacy" mean "religious legitimacy"?
4) Does "endearingly ambivalent" mean "self-contradictory but lovely"?

Background info:

First I should confess (that is probably the right word) that the
conference was sponsored by the Templeton Foundation. The
audience was a small number of hand-picked science journalists
from Britain and America. I was the token atheist among the
eighteen invited speakers. One of the journalists, John Horgan,
reported that they had each been paid the handsome sum of
$15,000 to attend the conference, on top of all expenses. This
surprised me. My long experience of academic conferences included
no instances where the audience (as opposed to the speakers) was
paid to attend. If I had known, my suspicions would immediately
have been aroused. Was Templeton using his money to suborn
science journalists and subvert their scientific integrity? John
Horgan later wondered the same thing and wrote an article about
his whole experience. In it he revealed, to my chagrin, that my
advertised involvement as a speaker had helped him and others to
overcome their doubts:
The British biologist Richard Dawkins, whose partici-
pation in the meeting helped convince me and other
fellows of its legitimacy, was the only speaker who
denounced religious beliefs as incompatible with science,
irrational, and harmful. The other speakers - three
agnostics, one Jew, a deist, and 12 Christians (a Muslim
philosopher canceled at the last minute) - offered a per-
spective clearly skewed in favor of religion and
Christianity.
Horgan's article is itself endearingly ambivalent. Despite his mis-
givings, there were aspects of the experience that he clearly valued
(and so did I, as will become apparent below). Horgan wrote:
My conversations with the faithful deepened my appreci-
ation of why some intelligent, well-educated people
embrace religion. One reporter discussed the experience
of speaking in tongues, and another described having an
intimate relationship with Jesus. My convictions did not
change, but others' did. At least one fellow said that his
faith was wavering as a result of Dawkins's dissection of
religion. And if the Templeton Foundation can help bring
about even such a tiny step toward my vision of a world
without religion, how bad can it be?