A TRACON Departure Controller reported Tower Controller issued a turn to a departure which placed it in to the path of an aircraft on final approach to an intersecting runway.

Narrative

Aircraft X requested runway XX; he was vfr and was told to make straight in. He was switched to tower who cleared Runway XYR for take off vfr to ZZZ. Without restrictions he turned on departure toward ZZZ straight into the face of the runway XX arrival. Closest proximity was 0 feet and 0.18 miles.This was the first event of many in a skill check session with a supervisor and local trainee plugged in. At this point the supervisor had taken over the session due to being above the trainees ability level and it snowballed after to have two other relatively close calls in under twenty minutes. As the radar controller I had to knee jerk react to multiple close calls that tower sent to departure with no coordination. Also after the fact I was told the tower in charge was instructed they did not need to monitor the local frequency because the 'supe had it'.I recommend two separate fixes: After near mid-air situations either pilot reported or controller observed relief should be made. There was zero situational awareness left between the supervisor or the trainee being skill checked and continuing to launch planes was dangerous and reckless.Two I recommend that as approved by the national .4 the supervisor complete their skill assessment from a monitor position not plugged in with the trainee due to not getting more than their minimum currency in the area and not being ready to provide positive control for the trainee when they meet the end of their abilities.