There are some meets that are free.
But usually the different flying clubs use the events as a way to raise money for the club. So they have a "landing fee" or something.
if the club is affiliated with the AMA, then yes you have to join the AMA to fly there and participate in the event.
if I remember right, the AMA keeps track of the scores and standings for competitors in some of the events, such as Pattern Flying. That is in order to separate the Novice, intermediate and advanced flyers from each other.
There are some clubs that are not affiliated with the AMA though. I don't know who they are, but I remember encountering a few over the years.
Quite a few of the RC car and RC boat clubs make one join the car or boat related racing organizations to compete in their events too. AMA membership is usually not needed for those unless it is a AMA meet.