What is the name of Hook's pirate ship and the skull and crossbones flag?
The two are the same thing: the flag of the skull and crossbones is the Jolly Roger, which is also the name of Hook's ship. Here's the quote from the book to back it up:
One green light squinting over Kidd's Creek, which is near the mouth of the pirate river, marked where the brig, the Jolly Roger, lay, low in the water; a rakish-looking craft foul to the hull, every beam in her destestable like ground strewn with mangled feathers.
Hope it helps!