the head administrator of the forum, is it by the person with most activity, by election or by appointment? and how is the position moderated? since the forum has no owner after the disappearance of Satoshi Nakamoto.

The active administrators are currently:
theymos (me)
Gavin Andresen
sirius

Sirius runs the server.

Of course not, do you really need to ask?

 - I was made a forum admin in 2011, after Satoshi left. (Silk Road also appeared after Satoshi left.) I didn't have any special access to bitcoin.org until around 2013, and in fact I didn't even have any access to the bitcointalk.org DNS until 2013.

There was a period where both Sirius and I were active administrators. For convenience, I reckon Jan 1, 2012 as when I became head administrator, though it was actually a gradual transition starting before and ending after that.

The story of how I became head admin is actually pretty boring. Moderators were needed, so I was made a global moderator. Then admins were needed, so I was made an admin. Then over time the other admins slowly lost interest and resigned until I was the only one left. I guess most of the people who were around here to see this have more-or-less left the community now. That's a bit sad.

It's not entirely clear, but for simplicity I usually say that I became head admin at the beginning of 2011, a little over a year after the forum was created.

The forum was originally located at bitcoin.org/smf, then forum.bitcoin.org (hence the redirect), and finally bitcointalk.org. Fun fact: The name "bitcointalk" was invented by Jeff Garzik, and he's the one who bought the domain.