#2, it’s not the magnitude of AoA which is the problem, it is if the control surface used for stall recovery (tail/elevator) is masked by the wing downwash and thus less effective.
#3 - #5, perhaps the main reason for having a stick push is that the aircraft’s natural stall warning or stall characteristics do not meet the certification requirements - particularly pitch down.
I do not recall that spin prevention specifically was considered. The aircraft will not spin unless stalled, stick push minimises the duration of a stall or avoids altogether.
Straight wing vs swept should not be an issue, the dominant factor is the inability to effect a nosedown pitching moment.
Both the BAe146 and HS125, relatively straight wing, were predicted to suffer deep stall based on wind tunnel testing. Both aircraft had stick pushers, but flight testing did not discover any deep stall situation.