Short answers, pulled from the story.
The original selective advantage offered by the vertebrate jaw may not have been related to feeding at all. Jaws are thought to have first functioned in the buccal pump, a mechanism that pushes water across the gills in fish or air into the lungs in amphibians. Feeding became a dominant function only later in evolutionary history.
The vertebrate jaw probably originally evolved in the Silurian period. It appeared in the Placoderm fish, which then diversified extensively during the Devonian period.
Arthropod jaws take the form of mandibles or chelicerae, depending on the group. Unlike vertebrate jaws, they are made of chitin and oppose laterally rather than vertically. Many mouthparts associated with arthropod jaws are thought to be modified legs.
Aristotle's lantern is the name for the jaw structure of sea urchins. It displays five-part symmetry, with each unit of the jaw holding a single continuously growing tooth composed of crystalline calcium carbonate.
Two bones that formed part of the jaw in reptilian ancestors, the articular bone of the lower jaw and the quadrate, were reduced in size and incorporated into the ear in mammals. This transition contributed to the hearing apparatus characteristic of the mammalian lineage.
The snake skull shows the greatest degree of cranial kinesis among tetrapods. This extreme flexibility of the jaw bones allows snakes to swallow prey items larger than their own heads.