An LPR is required to present an I-551 (Green Card) for reentry into the U.S. If you are not a U.S. citizen or a U.S. LPR, you will need a passport and/or the appropriate documentation based on the status you are seeking in the U.S. for any type of cruise, closed loop or not.
The Picard Maneuver is a battle tactic invented by Starfleet Captain Jean-Luc Picard. In 2355, Picard was in command of the USS Stargazer when it was attacked by an unknown alien vessel, later determined to be of Ferengi origin.
An officer who decided to use the Picard Maneuver would first order a sensor bearing to get the exact position of the opposing vessel. Then, the officer would order his or her helm officer to drop into high warp for a few seconds to close the distance between their ship and the opposing vessel.