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.
From Memory Alpha : The Picard Maneuver was born out of desperation during the battle. The Stargazer, which was damaged, suddenly accelerated into high warp directly towards the Ferengi ship. By doing so the Stargazer appeared to ship's sensors, for an instant, to be in two places at once.