Does anything in the play attest to Jason's background as a hero? Is the reader meant to sympathize with him? Barring their death cries, the children remain silent throughout the play. How does Euripides handle their characters in order to supply an element of pathos to their death? Include the meaning of the term "pathos" in the answer.

In Greek myth, Jason was a hero who led the Argonauts on a quest to retrieve the Golden Fleece for the king of Iolcus, Pelias. On this journey, Jason met the sorceress Medea, and the two eventually were married and bore two children.
When Jason meets with Medea after she is exiled by Creon, the two of them argue over Jason and the Argonauts' exploits while finding the Golden Fleece. Specifically, Medea brings up the dragon that guarded the fleece and explains that she was the one who killed the beast so that Jason could move onwards. From Medea's perspective, Jason's heroic stature is (at least partially) undeserved; her actions were essential in Jason's quest, but she hasn't received any of the credit for it.
Jason, however, refuses to acknowledge her role in the journey. One possible reason for this is Medea's status as a "barbarian" to the people of Corinth. Medea left behind her own people to be with Jason, and we get the sense that she is seen by the Corinthians as somewhat of an outsider. Jason might be downplaying Medea's role in his quest in order to appeal to the Corinthians more.
I don't believe that we're meant to sympathize with Jason, as ultimately it is his decisions that precipitate Medea murdering Glauce, Creon, and their children. Jason believes that he abandoned Medea with the right intentions and that marrying Glauce will allow him to provide for Medea and their children while keeping his position with the Corinthian people in check. But even if Jason's intentions were fine, the fact that he doesn't communicate these plans to Medea beforehand makes him unlikable.
Through all the drama that unfolds, the children of Medea and Jason remain silent. They often play with toys away from the central part of the scene. The characters with speaking roles may elicit our sympathy or anger by their actions, but the children demonstrate the play's use of pathos by their inaction.
"Pathos" is a classical rhetoric technique that appeals to the audience's emotions. In plays, as well as other types of media, pathos is used to drum up feelings in the audience and keep them invested emotionally in what's being performed. We judge the other characters in Medea based on what they've done and what they say; we determine whether or not they're innocent. But the children remain innocent throughout the story. They've done nothing wrong; they're simply victims of the unfortunate circumstances that their parents have brought about. Thus, when they die, their screams represent the innocent lives that have been destroyed thanks to the actions of Medea, Jason, Creon, and so on.