What do the Christmas tree and the Christmas presents represent?
The Christmas tree, which is to be hidden from the children for now, is symbolic of Nora and Torvald's relationship. She is keeping a secret from him.
The Christmas presents show the inequity of the marriage. Nora spends money, and is chided by Torvald for it. She even asks that he give her money as a Christmas "gift". He has the upper hand in this marriage, and she must beg for money to provide Christmas for their family.