Based on the information provided in your questions and the video transcript, here are the correct responses:
Question 1:
The Cherokee took their case (Worcester vs. Georgia) to the U.S. Supreme Court, who ruled that:
Response: the Cherokee Nation had a right to their land, and the State of Georgia should not try to take it.
Question 2:
True or False: President Andrew Jackson refused to support the U.S. Supreme Court's decision in Worcester vs. Georgia.
Response: True.