Short answers, pulled from the story.
Hayreddin Barbarossa was an Ottoman corsair and grand admiral born on the island of Lesbos around 1466-1483. He secured Ottoman dominance over the Mediterranean during the mid-16th century through a series of naval victories, most notably the Battle of Preveza in 1538, which kept the Ottomans supreme at sea for 33 years until the Battle of Lepanto in 1571.
The name Barbarossa, meaning Redbeard in Italian, originated as a corruption of the honorific Baba Oruç, which was given to Hayreddin's brother Oruç Reis for transporting Muslim Mudejars from Christian Spain to North Africa between 1504 and 1510. Spanish, French, and Italian speakers transformed Baba Oruç into Barbarossa due to the similarity in sound. Hayreddin inherited the name after his brother died in 1518.
Barbarossa was appointed Kapudan-i Derya, meaning Grand Admiral, of the Ottoman Navy by Sultan Suleiman the Magnificent in 1532, after being summoned to Constantinople and received at Topkapı Palace. He also received the title Beylerbey of North Africa at the same time.
At the Battle of Preveza in September 1538, Barbarossa's forces led by Sinan Reis defeated the combined fleet of the Holy League, which was commanded by Andrea Doria and composed of the Papacy, Spain, the Holy Roman Empire, Venice, and the Maltese Knights. The victory secured Ottoman control of the Mediterranean for the following 33 years.
In 1543, Barbarossa sailed to assist France, then an Ottoman ally, against the Habsburgs with a fleet of 210 ships carrying 30,000 Ottoman troops. He captured Nice on the 5th of August 1543 on behalf of King Francis I, and King Francis placed the city of Toulon under his control for six months, during which it operated as a Turkish city with its own mosque and slave market.
Barbarossa is buried in a mausoleum in the Barbaros Park of the Beşiktaş district on the European side of Istanbul. The mausoleum was built in 1541 by the architect Mimar Sinan at the site where the Ottoman fleet used to assemble, and a memorial was erected beside it in 1944.