I suspect most of the ships were beached when not in use, and/or tied onshore or close to shore to keep them from drifting off. The ships were build with some kind of truss system to lighten them, which one reason they achieved the velocity for effective ramming. Adding more rows of rowers turned into a bit of an arms race, with the final iteration being a vessel so large it never saw combat. According to Casson, it was a marvel of its age, and after the Romans conquered Greece, they were so taken they towed it to Rome as a trophy and tourist attraction.
The Carthaginians relied for the most part on mercenaries, and the classical period Greek city-states (which are basically coeval) used paid rowers after that initial period when they defeated Persia. Carthage also built a large navy and a harbor facility that served both their military and their commercial needs.
http://www.google.com/search?q=carthage+harbor&sa=X&oi=image_result_group&tbm=isch
That answered the need for beaching them in some fashion but why the roofs. Ah ha, thee hot summer sun promoting mold etc. Thus the cover, much like the ubiquitous blue tarps at modern marinas. Video mentions hull plank shrinkage at joints that most likely required required re-caulking, but that's always been SOP for wooden ships.
Optimum hull shape for speed IIRC, is light, long, slender, and shallow draft, like racing sculls and Viking like boats.
Always wondered about the triremes efficiency, where stroke timing must be precise. Came to the conclusion that the sudden burst of ramming speed and mass gave them the ship killing power.
The video also provides a full count of the boat sheds as distributed between the three protected harbors, illustrated by the drawings. Impressive concentrated and coordinated effort by the fractious Greeks. In addition to the warning, Beware of Greeks bearing gifts, the adversaries added, Beware of Greek ship bearings. ;>)