Short answers, pulled from the story.
Sigismund I the Old was King of Poland and Grand Duke of Lithuania from 1506 until his death on the 1st of April 1548. He was a member of the Jagiellonian dynasty, the fifth son of Casimir IV, and came to power at the age of thirty-nine after both of his reigning brothers died in quick succession.
The Prussian Homage was a ceremony in which Sigismund's nephew Albert, Duke of Prussia, paid feudal homage to Sigismund following the Treaty of Kraków in 1525. Albert had converted to Lutheranism under the persuasion of Martin Luther and received the secularised Teutonic Order's territories as the First Duke of Prussia. The arrangement required Albert and his Protestant successors to continue paying tribute to Polish monarchs until the Treaty of Bromberg in 1657.
The Chicken War was an anti-royalist revolt by the Polish nobility at Lwów in 1537. The rebels presented Sigismund with thirty-six demands, including a halt to Queen Bona's land acquisitions and the adoption of a rule called Incompatibilitas preventing individuals from holding multiple official positions. Sigismund rejected most of the demands, and the rebellion dispersed having achieved little; the name was coined mockingly by magnates who supported the king.
Bona Sforza was the daughter of Gian Galeazzo Sforza, Duke of Milan, and became Sigismund's second wife in 1517. She brought Italian artists, architects, and sculptors to Poland, drove the expansion of royal estates, and was instrumental in developing both the Polish Renaissance and a Franco-Polish diplomatic alliance aimed at recovering Milan.
The Sigismund Chapel is a funerary monument built between 1519 and 1533 according to plans by Bartolomeo Berrecci of Florence, serving as a mausoleum for the last Jagiellons. Its exterior dome is gold-plated and its interior marble tombs were designed by Santi Gucci. Historians and architects have described it as the most beautiful example of the Tuscan Renaissance north of the Alps.
Sigismund I the Old died on the 1st of April 1548, Easter day, at the age of eighty-one, after years of gout, rheumatism, and recurring fevers. He was buried on the 7th of July at Wawel Cathedral in Kraków. His only surviving legitimate son, Sigismund II Augustus, succeeded him and became the last Jagiellon king of Poland.