Are Elijah and Jesus prophets, and what is their story if they are?

"Jesus" is the name given by Christians to the Prophet Eisa, peace be upon him. As for "Iliya'," it is the name of the city of Jerusalem, and its meaning is "House of God." It was mentioned in prophetic narrations such as: "Journeys are undertaken only to three mosques: the Mosque of the Kaaba, my Mosque, and the Mosque of Iliya'."