Reflection on Our Lady of Mt. Carmel

How did the title of Our Lady of Mt. Carmel come about?  What is the connection with the Prophet Elijah?  How did the spirituality of Elijah spread across the world?  What happened on July 16th that is so significant to Carmelites?  What is the connection of Our Lady of Mt. Carmel to the Church approved apparitions of Our Lady in Lourdes and in Fatima?  How are we connected today?