Mark- Concerning the movement of the ship, on the maiden voyage there was some talk amongst the crew of short cruises being made for the US travel agents and press. Don't know how true that was, but it might explain what you saw.
Concerning the parking decks being open for viewing, I'd say "maybe or maybe not." Security on the first voyage was extremely tight in some places and not as tight in others:
Southampton: No admission to pier area and terminal complex pre-sailing. On sailing day taxis and cars for passengers were allowed in, but we were not allowed out of the terminal to see the ship once we entered. Best, in fact only, close view of the ship available to theh general public was from the various ferries which passed.
Madeira: Passengers had free access to the pier, but there were two separate security checkpoints one had to pass through if one returned to the pier, as we did, on foot. Best available general view of the ship was from the beach we were moored opposite, probably 300 yards away. Police craft kept boats at a distance, although once we sailed private craft were able to get VERY close.
Tenerife: We were moored at the furthest extent of a very long pier complex, and the general public was allowed to get fairly close to the ship- there was a barrier and checkpoint about a hundred feet forward of our bow, and a correpsonding barrier atop the harbor wall, but those who cared to make the walk had a fairly good unobstructed view of the ship. Police boats kept harbor craft at bay.
Las Palmas: Entire pier complex was open to the general public, and if there was security it was VERY discreet. Subsequently, this was the only 'fun' port we were in- the empty terminals in the other ports became progressively drearier.
Barbados. Pier and harbor wall complex may or may not have been guarded. It was hard to tell.
St. Thomas: Moored out side the harbor and passengers brought in by tender. Late in the day we were circled by a helicopter, and by several police boats and Coast Guard Vessels which kept the general public at a great distance.
Fort Lauderdale: No public access.
So, don't count on being able to access the parking decks. I don't see how they can close down the whole pier complex 'though, so the best photos you'll likely get will be from the sidewalk on the lower level of the terminal complex, between piers. Bring at least two lenses, because if there is a ship moored opposite her it might be difficult to frame a bow-to-stern shot wihtout the aid of a wider angle than a standard lens gives.