Short answers, pulled from the story.
Hemchandra emerged from Rewari as an old Hindu associate of Sher Shah Suri who climbed from humble circumstances to become Adil Shah's Chief Minister and general of the Suri army. He claimed royal status assuming the title of Vikramaditya or Bikramjit after defeating Mughal forces at Tughlaqabad on the 7th of October 1556.
The battle occurred shortly after the 7th of October 1556 when Hemchandra took possession of Delhi following his victory at Tughlaqabad. The engagement itself happened later that same month during the Mughal conquest of the Sur Empire.
The two armies clashed at Panipat not far from the site of the First Battle of Panipat of 1526. The location featured a deep ravine where neither Hemchandra's elephant nor horse units could cross to reach their opponents.
Hemchandra was wounded when struck in the eye by a chance Mughal arrow which caused him to collapse unconscious on the battlefield. His death triggered panic in his army and led to the capture of the elephant carrying him before he was beheaded according to contemporary writer Muhammad Arif Qandhari.
Ali Quli Khan Shaibani captured an entire train of artillery from the Afghans who abandoned the guns and fled without making a stand. This loss proved costly for Hemu as his army had no artillery during the specific battle despite counting among its ranks a 30,000-strong cavalry force and 500 war elephants.