Do I have to be there the entire seven days to play the open?

The schedules are the seven-day, five-day, and four-day options. The shorter schedules use faster time controls in the first 5-6 rounds. 

The U.S. Open itself is one large open tournament with no "under" sections. The three schedules merge beginning on August 1 for round 7. 

The full breakdown of round times, by schedule, can be found here. Round times, by schedule, are also reflected on the daily schedule view.