Click here: Society of Saint Pius X (in the United States).
That would be greatly overblown. The SSPX doesn’t use brainwashing techniques, just simple indoctrination like everyone else. Adults are free to choose whether the follow the tenets of their beliefs or not.
Officially, no. There are a significant number of priests and laity within the SSPX who privately are sedevacantists, though.
No, they do not have their own pope. They recognize Pope Benedict XVI as a valid pope, but they have disagreements with him and the current Church government.
The Catholic Church would never recognize two popes being simultaneously valid. Throughout the history of the Church, sincere Catholics have from time to time had difficulties recognizing which contender or the other was the true pope, but the Church has always had only one pope at a time.
There have been many threads here at the Catholic Answers Forum about the SSPX that you might find using the search function.