If a parent dies within the month leading up to Rosh Hashana, I was told that you close the thirty days at that point. What is the law regarding the end of month shiva if it falls after rosh hashana?

It is unimportant. The mourning over a person who passed away more than a week prior to Rosh Hashanah, stops when Rosh Hashanah arrives. Rabbi Ro'i Margalit