"Walking the Plank" is a Hollywood myth. Pirates were more likely to throw men overboard, hang them from the yardarms, or keelhaul them.
Every Pirate Captain established a set of rules called the "Articles." Every member of the crew signed articles of piracy over a boarding axe prior to setting sail - symbolic to the oath the pirate just promised his fellow sailors.
"Davy Jones' Locker" is a nautical term dating back to the 1700s. Davy Jones was sailor slang for the Devil, who resided at the bottom of the sea. So to send someone to Davy Jones' Locker meant killing the person.
Pirates burying their treasure were an exception, not the rule. They didn't expect to live very long and usually spent their share of the plunder on liquor, games of chance, and women.