Yes, "того" is often used in colloquial speech as interjection while trying to formulate the idea (or to avoid the formulation for some reason). Here they want to avoid words like "fired". The reply just monkeys.

"Заявка" is a request. Emergency staff called to police and gave a request about a violent injury. The police officer in charge should go there and proceed the event officially (оформить). But officer in charge is busy with another request so the dispatcher asks someone else...