These terms are important aspects of Jewish history and Jewish law. First, Shulcan Aruch is the established legal code of Jewish Law. It was established in the 1500s by Rabbi Joseph Caro.
Halacha is Jewish law. Halacha describes the way observant Jews carry out various commandments and rituals. For example, halacha will describe how to light Shabbat candles, including how to say the blessings.
Menashe ben Israel was born in Amsterdam in the 17th century. He persuaded Oliver Cromwell to allow Jews to return to England.
Rabbi Isaac Luria was a famous Kabbalist who lived in the 16th century. He was also known as HaAri. He is credited with establishing the Kabbalah, which is the study of Jewish mysticism.
Chiemelnicki lived in Poland in the 17th century. He was a huge anti-Semite and initiated a series of huge pogroms against the Jews. Over 100,000 Jews were killed during his reign of terror. In reaction to Chiemlnicki, there arose a man named Shabetai Zevi, who proclaimed that himself the Jewish Messiah. Nathan of Gaza was one of his followers.
The Besht is better known as the Baal Shem Tov (Hebrew for good name), the founder of Chassidism. The mitnagdim were the opponents of Chassidism. Chassidism stressed finding G-d through personal experiences and mysticism. The mitnagdim stressed learning and following ritual.