Short answers, pulled from the story.
The Empire of Nicaea began in 1204 when Theodore I Laskaris fled to Nicaea after the crusader invasion of Constantinople. The state effectively ended in 1337 when Nicomedia fell to Turkish forces, though its imperial status concluded with the restoration of Byzantium in 1261.
Theodore I Laskaris founded the Empire of Nicaea as the son-in-law of Emperor Alexios III Angelos. He proclaimed himself emperor after fleeing Constantinople following the flight of Byzantine emperor Alexios V Doukas Mourtzouphlos.
Michael VIII Palaiologos restored the Byzantine Empire by allying with Genoa and sending general Alexios Strategopoulos to capture Constantinople in July 1261. Strategopoulos convinced guards to open the gates while most of the Latin army fought elsewhere, allowing him to burn the Venetian quarter and claim victory for Michael.
John IV Laskaris was blinded on his eleventh birthday, the 25th of December 1261, on orders from Michael VIII Palaiologos to make him ineligible for the throne. He was subsequently exiled and imprisoned in a fortress in Bithynia.
After 1261, soldiers were transferred from Asia Minor to Europe to fund wars against Latin states and Epirus, leaving the old frontier relatively undefended. Raids by Turkish ghazis went unchecked until they turned into permanent settlement and conquered nearly the whole region by c. 1300.