A passenger on the Mayflower named John Howland got thrown off the ship during a violent storm, but grabbed ahold of topsail halyard and was pulled back on to the ship safely.
After the Puritans arrive at Cape Cod, they try to communicate with the Native Americans to see if they spoke some English and also to find out if they were going to attack them. In addition to that, the Puritans knew that the Native Americans knew the lay of the land, so they followed them in order to find food and wate.
During the Puritans first harsh winter in 1620, due to the lack of food, water, and medicine, many died and became sick. However, the healthy Puritans took care of the sick and dying by doing for example, helping them do their many chores and tasks for them, instead of just leaving them out to die.