Anyone who believes in false gods, false prophets, or false Messiahs is not a Karaite. Believing in a false prophet is a form of idolatry no less insidious than believing in the Talmud, and perhaps more so. Women have equal status to men in Karaism. When the Torah commanded that the entire nation come to hear the Torah read in a public reading on Sukkot every seventh year, it explicitly mentioned that both men and women were required to come and learn the Torah. Women have an equal obligation to keep the commandments and study the Tanach.
Women have equal standing and participation in prayer services and as spiritual leaders.
Karaites do not bring sacrifices today in the absence of the Temple. That is the Samaritans, not the Karaites. The Samaritans believe in the holiness of Mt. Gerizim while Karaites believe in the holiness of Jerusalem. The Samaritan Torah has minor differences from the Jewish Torah. Karaites accept the same Torah as all other Jews and in fact it was Karaites scribes who preserved the Torah used today by all Jews.