Short answers, pulled from the story.
Emperor Charles V granted Malta, Gozo, and the North African port of Tripoli to the Order of Saint John in 1530 in exchange for an annual payment of a single Maltese falcon, delivered each year on All Souls' Day to the Viceroy of Sicily. The Order had been left without a base after the Ottoman siege expelled them from Rhodes in 1522.
The Ottoman force of roughly 40,000 men besieged approximately 700 knights and 8,000 soldiers. Grand Master Jean Parisot de Valette refused to abandon the fortifications despite heavy losses. The Ottomans broke off the siege on the 8th of September 1565 after Sicilian reinforcements landed at Mellieħa Bay; of the Ottoman force at its peak, only around 15,000 returned to Constantinople.
Yes. On the 21st of May 1651, the Order acquired four Caribbean islands: Saint Barthélemy, Saint Christopher, Saint Croix, and Saint Martin, purchased from the dissolved French Company of the American Islands. The Order administered them under the governorship of Phillippe de Longvilliers de Poincy until his death, then sold all four to the French West India Company in 1665.
By 1798, the Order was financially bankrupt, its revenues in France having been seized by the revolutionary French government in 1792. When Napoleon arrived in June 1798, the knights surrendered almost without resistance despite having fortifications capable of sustaining a long siege, ending over two and a half centuries of Hospitaller rule.
The Maltese corso was the Order's sustained naval campaign against Ottoman shipping in the Mediterranean, conducted from 1530 to 1798 and reaching its peak between 1660 and 1675. It served as a major source of income for the Order and employment for the local Maltese population, generating revenue through plundered goods and the capture of Muslim slaves.
After losing Malta, the Order dispersed across Europe and its last formal territory, the Principality of Heitersheim, was annexed by the Grand Duchy of Baden just months before the Holy Roman Empire dissolved on the 12th of June 1806. In 1834, the Order established its headquarters in its former embassy in Rome, where it continues today as the Sovereign Military Order of Malta.