Short answers, pulled from the story.
The Latin Empire was a feudal Crusader state founded by leaders of the Fourth Crusade on territory seized from the Byzantine Empire. It existed from 1204 to 1261, when the Nicaean general Alexios Strategopoulos retook Constantinople and restored Byzantine rule under Michael VIII Palaiologos.
The Fourth Crusade had been called to retake Jerusalem, but economic and political pressures redirected it. The Crusaders became involved in a Byzantine succession dispute, promised financial support by Alexios IV Angelos in exchange for restoring his father Isaac II to the throne. When those payments did not materialize after Isaac and Alexios IV briefly ruled, the Crusaders sacked Constantinople in April 1204.
Baldwin IX of Flanders was elected the first Latin Emperor on the 9th of May 1204 and crowned on the 16th of May in the Hagia Sophia in a ceremony that closely followed Eastern Roman practices. He was captured at the Battle of Adrianople on the 14th of April 1205 and died later that year imprisoned in the Bulgarian capital Tarnovo.
The Nicaean general Alexios Strategopoulos entered Constantinople on the night of the 24th and the 25th of July 1261 with only about 800 soldiers. He learned that the Latin garrison and Venetian fleet were absent raiding the island of Daphnousia, used a secret passage to breach the walls, and seized the city. Emperor Baldwin II fled to the harbors and escaped by ship, ending the Latin Empire.
The Latins dismantled the Greek economic administration immediately after the conquest, disrupting production and trade from the outset. By the 1230s Constantinople faced shortages of basic foodstuffs. Baldwin II was reduced to selling looted relics, stripping the lead roofs of the Great Palace, and even pledging his only son Philip to Venetian merchants as loan collateral.
Crusader rule over Constantinople brought western artists into contact with Byzantine visual culture and contributed to the Italo-Byzantine style. The Italian painting Virgin and Child by Berlinghiero, made around 1230, was modeled on a Byzantine icon type called the Hodegetria. André Grabar attributed the near-total absence of art produced within the Latin Empire itself to destruction and the disruption of the Greek clergy who had sustained artistic production.