Short answers, pulled from the story.
The Empire of Nicaea was the largest of three Byzantine successor states founded after the Sack of Constantinople in 1204, when Western European and Venetian forces seized the city during the Fourth Crusade. It was founded by the Laskaris family and lasted from 1204 to 1261, when it restored the Byzantine Empire by recapturing Constantinople.
The Empire of Nicaea was founded by the Laskaris family, beginning with Theodore I Laskaris, the son-in-law of Byzantine emperor Alexios III Angelos. Theodore fled Constantinople after the crusader invasion of 1204 and established himself at Nicaea in Bithynia, assuming the traditional Byzantine imperial titles in 1205.
Emperor Michael VIII Palaiologos allied with Genoa against their shared enemy Venice. His general Alexios Strategopoulos spent months observing Constantinople's defenses, and in July 1261, while most of the Latin army was fighting elsewhere, he persuaded the city's guards to open the gates. Michael was recognized as emperor a few weeks later, ending fifty-seven years of Latin rule.
John IV Laskaris, the young Nicene emperor whom Michael VIII Palaiologos displaced, was left behind at Nicaea. On the 25th of December 1261, on his eleventh birthday, Michael had him blinded, rendering him ineligible for the throne by Byzantine custom. John was then exiled and imprisoned in a fortress in Bithynia, and the act provoked his excommunication of Michael by Patriarch Arsenios Autoreianos.
After the restoration of Byzantine Constantinople, the former Nicene territories in Asia Minor were stripped of wealth and soldiers to rebuild the capital and fund European wars. Turkish raids went unchecked, and by around 1300 nearly all of the former empire's land had been conquered by the Turks. Bursa fell in 1326, the city of Nicaea itself in 1331, and Nicomedia in 1337.
At the Nicene court, writers and church leaders began using the terms Hellenes and Graikoi to describe the Greek-speaking population, shifting away from the traditional Roman identity. Scholars such as A. E. Vacalopoulos see this period as the genesis of Greek nationalism, while Roderick Beaton argues it represents an embryonic ethnic awareness centered on language rather than full nationalism. Most of these ideological innovations were set aside when Michael VIII restored Byzantine Constantinople and returned to older Roman imperial rhetoric.