Use the radar all the time. Tough to do if in a turn practicing instruments and single seat. The pilot was probably heads out looking for the aircraft. Could have switched to a visual acquisition mode, but probably task saturated at that point. Also may have been futile if he was in a turn and the Cesna was climbing.

Midairs happen all the time, at least a few a year. Usually this is in dynamic situations (BFM, etc) or joins, especially at night. Usually between fighters and seldom with civilians.