1: Many Jews have a custom not to learn Torah on the night preceding December twenty-fifth. This night is referred to as Nittel Nacht. (See Netai Gavriel Chanuka 385-418 for a full discussion) Most, however, learn Torah on Nittel Nacht. For practical halacha, one should follow his or her custom and consult a rav.
2: Some poskim question whether one may marry on Nittel Nacht. (See Shulchan Haezer vol. 2 page 88b) The Netai Gavriel (Nisuin chapter 48 note 45) cites the Sefer Chazon Yeshayahu who reports that the Satmar Rebbe zt”l was against arranging weddings on this night.
However, the Sefer Shulchan Haezer notes that two great rabbanim made weddings on Nittel Nacht. He adds that one of the rabbanim was a grandchild of the Chasam Sofer, and that perhaps he had a tradition from his grandfather to permit marriage on Nittel Nacht. The Netai Gavriel adds that the accepted custom in Israel is to rule leniently and allow for weddings to take place on Nittel Nacht. This was also the view of Harav Yosef Shalom Elyashiv zt”l. (Yevakshu Mipihu page 419) A similar permissible view can be found in the Sefer Yalkut Yosef. (Sovea Semachos page 43)