at the school i went to, homecoming was around the beginning of the schoolyear and was open for all grades. prom is around the end of the schoolyear and is grade exclusive. only 11th and 12th graders have them and they have their separate proms. both homecoming and prom you have to pay to go to.
about the homecoming king/queen you mentioned too. i never went to homecoming but at least at prom people sign up to be candidates for prom court and then prom attendees vote on who they want to be prom king and prom queen (those who apply for it don't do it in pairs so two people that don't know each other could be elected) and then they share a dance where everyone awkwardly watches.