You cannot trim down in the NG while there is control wheel backpressure in manual flight. Which is what you would naturally do to keep your attitude.
Yes.But activating the under-floor cutout feature requires a pronounced opposing stick force.
If accidental nose down trim went unchecked for longer than say,several seconds at that altitude,they wouldnt have had a lot of room to play with.It remains a possible scenario.More data is needed to narrow it down.