I think the "send me all new questions" idea is great. I would add
that it could be even better if the message with the new question
contained a "Notify me of new answers" hyperlink in it. That way,
if the question looks intriguing, you could subscribe with one
click.
Beyond that, I think we're on the right track in terms of using the
FAQ module. Scoping it to assign admin privileges on individual
FAQs and adding an "Add this to the FAQ" hyperlink to ad_footer
for FAQ admins would both be very helpful. Later on, it would be
nice to assign categories to FAQs so we can group them, but
that's not an immediate pressing need.