Short answers, pulled from the story.
Muhammad Sultan Mirza was appointed governor of Tabriz, the capital of the Jalairid Sultanate, when he was only ten years old. This early assignment placed a child in charge of a major urban center while the rest of the empire remained unstable.
Muhammad Sultan Mirza died on the 12th of March 1403 near the city of Afyonkarahisar while suffering from injuries sustained in battle. He fell seriously ill during a journey back through Ankara after the Battle of Ankara.
Muhammad Sultan Mirza led the main body of the army during the Battle of Ankara on the 20th of July 1402. Ottoman forces suffered a decisive defeat and Bayezid himself was taken captive soon after this engagement.
Timur chose Muhammad Sultan Mirza as heir apparent based primarily on his birth status because his father Jahangir alone among Timur's four sons was born of a free-wife rather than a concubine. This maternal lineage gave him an exalted status among potential successors.
Muhammad Sultan Mirza built a fort in the region of Ashapara followed by another further east by the Issyk-Kul lake to secure the eastern province of Ferghana. These structures were intended to serve as a frontier line for operations against Moghulistan.