I've read in many places that he was hesitant to punish his killers, which eventually led to the fitnah and then his own death. If he'd had punished them possibly the battle of Karbala could've been averted. So can anyone please tell?

As probably many of you are aware, at the time of Imam Hussain (a.s.) there was a tragedy event which was/is famous as "Battle-of-Karbala". It is as follow: - www.al-islam.org/the-tragedy-of-karbala But the question which I am looking for, is that who the name of the oldest person of Battle-of-Karbala (as the soldier of Imam Hussain (a.s.)) was who was martyred during the battle.

During and in the aftermath of the Battle of Karbala where was Muhammad al-Baqir (as)? And under whose care? Seeing from his date of birth and the year in which the Battle of Karbala took place (source: Wikipedia) he was 3-4 years old at the time.