Is staying for four hours in Mina, moving around in it due to overcrowding and the absence of a designated spot, sufficient for the obligatory stay there, and does this entail an expiation or an incomplete Hajj?

Staying overnight in Mina during the days of Tashreeq is one of the obligatory rites of Hajj, and it is achieved by remaining there for more than half the night. If you spend more than half the night in Mina, you have fulfilled the obligation. However, if you do not spend more than half the night, you have neglected the obligatory overnight stay. If this occurs on all nights, a sacrifice (dam) is required of you. But if it is for only one night, it suffices to feed a poor person a mudd of food.