Dead Man's Chest is the sequel Curse of the Black Pearl, followed by Uncharted Waters (rumored)
Keith Richards has been touring with the Rolling Stones, not filming. He is however Depp's supposed inspiration for Captain Jack.
From what I have read:
Bootstrap Bill was thrown into the water, but he was also cursed. He sold his soul to Davy Jones to escape the agony of dealing being stuck underwater for eternity.
Will and Elizabeth do have a wedding. This is when Jack comes crashing in.
Jack dies and meets Barbosa at the end, leading into 3.