Like any club or group, it really depends on who comprises your local group. We used to have an active Mensa group (yes, I am a member). The head dude recruited a variety of cool speakers to come to the meetings. We had a really nice 'reptile' lady one night. She brought snakes/turtles/etc and gave an interesting speech.
He stepped down, and now all we do is meet and eat at some restaurant. I've only been to one of the 'new' meetings in the past 8 years probably.
Qualification is based on a variety of tests. Some tests are excluded now as the tests have evolved. Typically 'achievement' test are excluded, whereas 'aptitude' tests are allowed.
I don't know if study would help pass, but it couldn't hurt.
It's not the type thing you tell someone. Other than my wife, NOBODY knows.
It does make for some interesting conversations sometimes.
For whatever reason, a large % of the people in the group here are govt employees.
Last thing, and the most interesting... people get in that aren't what you think of as highly intelligent. Sure, there's always the guy that can compete on Jeopardy, but some people are really gifted in ways that aren't apparent.