Short answers, pulled from the story.
Muhammad Sultan Mirza died on the 12th of March 1403, near the city of Afyonkarahisar, at the age of twenty-eight. He died from injuries sustained at the Battle of Ankara. His grandfather Timur ordered the entire army into mourning, with soldiers dressed in dark clothing.
Muhammad Sultan Mirza commanded the main body of the Timurid army at the Battle of Ankara on the 20th of July 1402. The Ottoman forces were decisively defeated and Sultan Bayezid I was taken captive shortly after the battle.
Timur's choice rested primarily on lineage. Muhammad Sultan's father Jahangir was the only one of Timur's four sons born of a free-wife rather than a concubine, and the prince's maternal descent traced back to Jani Beg, Khan of the Golden Horde. Position and battlefield accomplishment played secondary roles in the selection.
The Gur-i-Amir is a mausoleum in Samarqand that became the burial place of the Timurid dynasty. It was originally built for Muhammad Sultan Mirza alone. After Timur died in 1405, he was buried there alongside his grandson, and around 1409 Shah Rukh moved both bodies to the Gur-i-Amir.
Muhammad Sultan Mirza held the title 'Vali al-lakhd,' meaning throne-heir. Coins struck in Delhi after its conquest in December 1398 bore his name and this title, listed after that of Timur and the puppet Chagatai Khan.
Capturing Kamakh in 1402 provoked Sultan Bayezid I, who had recently seized the fortress from Timur's ally Taharten. The confrontation escalated into the Battle of Ankara on the 20th of July 1402, which ended in an Ottoman defeat and Bayezid's capture.