Agreed, there is no need to use the pad. Most operators in Turkey use the runway, saves time and stops half the pax from standing up after touchdown!
They were doing the backtrack turn (as post 70) and put the nosewheel on the grass, at that point they would have had no nosewheel steering to speak of. Then symmetric thrust just carried them straight on over the edge at taxi speed.
Unlikely, the turn would be to the right then left, which would put the aircraft the other way round. Also there is a about 10 metres plus of land between the runway edge and the escarpment at Trabzon, hence if the nose wheel went on the mud, they would just stop. Turkish TV records passengers saying aircraft was sliding and twisting before a loud crash and rapid nose down attitude.