Short answers, pulled from the story.
Emperor Charles V handed the islands of Malta and Gozo to the Order of St. John in 1530. This transfer followed a seven-year period where the Knights wandered Europe after losing their base on Rhodes in 1522.
Suleiman launched an invasion force of about 40,000 men against Malta in 1565. The defenders numbered only 700 knights and 8,000 soldiers, and half the knights died before the Ottomans left on the 8th of September having lost thousands of troops.
The Order began constructing Valletta as their new capital after the Great Siege. This city became headquarters in 1571 and remains Malta's capital today.
On the 21st of May 1651, the Order acquired four Caribbean islands: Saint Barthélemy, Saint Christopher, Saint Croix, and Saint Martin. These territories were purchased from the French Company of the American Islands which had just dissolved.
Napoleon landed in Malta in June 1798 despite the knights' ability to withstand a long siege because financial mismanagement made the Order unpopular with the Maltese population. They surrendered the island almost without fighting due to weakened conditions.