Answer:
For the first question: The government made land further to the west cheap, using that to persuade people to move.
For the second: For the first period of time, the relationships between the settlers and the Native Americans were good, with lots of trade, but it continued to be more and more strained as more Americans showed up, using more land and resources than was sustainable.
For the third: The Trail of Tears was a trek made by Native Americans away from their land and onto reservations, forced by the American government. Many many people died of illness, exhaustion, or were killed by the American soldiers forcing them along.
For the fourth: Every state was allowed to make their own laws about slavery as the US expanded westward.