I expect that the answer to that last question changes based on location. Local Mensa groups are made up of whoever in the local area decided to join, and their activities are whatever it is those members have decided to put their energy into doing.
I made friends with some members, who recruited me to join, and I found myself invited as a guest to an Annual Gathering (it just happened to be nearby), a Regional Gathering, and a local event in the process. I was in my mid-20s at the time, and nearly everyone at all of the events was at least twice my age, so it wasn't the kind of success in finding peers as I would have liked. There was nary a child to be seen.
One benefit: at presentations in the gatherings, the quality of questions from the audience was OUTSTANDING.
My DW-to-be attended the local event with me, and she found the experience extremely off-putting, with too many people in the room trying too hard to demonstrate how smart they were. I got the same vibe, at times. So we don't even think about it as an option for our DD... even though we're no longer in that same area.
