Short answers, pulled from the story.
Pope Innocent III approved the Franciscan order in 1209 after hearing their story. This approval came shortly after Francis of Assisi gathered eleven companions to live together in the deserted leper colony of Rivo Torto near Assisi.
Matteo Serafini founded the Order of Friars Minor Capuchin in 1525 as the youngest branch of the Franciscans. The group received early recognition and grew fast first in Italy then all over Europe after 1574 before becoming a separate order in 1619.
Brother Elias did not depose John of Parma; instead, the general chapter held in Rome under Gregory IX in 1239 deposed Elias. Albert of Pisa replaced him as Minister General at that same chapter which introduced General Statutes governing the Order.
Three Flemish friars reached central highlands in 1523 including Juan de Ayora, Pedro de Tecto, and Pedro de Gante. Fray Pedro de Gante initiated evangelization and studied Nahuatl language through contacts with children from Tetzcoco.
Pope Clement VI declared them official custodians of Holy Places in 1342. This Custody remains in force today following the acquisition of the Cenacle by King Robert of Anjou and Queen Sancha in 1335.