Would really like more information on this group. Do you have any recommendations?
or The History of the Jewish People by Moses Shulvas
There are only a few thousands of Karaites, who almost all live in Israel. They should not be confused with Christian heretics who CLAIM to be Karaites but have no historic connection.
Lots of web information about real Karaites on the web, as long as Christian interpretations are noted.
As with anyone who is thought to be or claims to be Jewish, the official determination (such as for marriage) is made on a case-by-case basis.