Maybe, Maybe not (most likely in your specific scenario).

I don't call a PC just because A1's shoulder is down and it contacts B1. B1 still has to be in the path legally...and B1 wasn't in this case.

That said, if A1 just blasts B1 for the sake of blasting B1 as your scenario suggests, PC.

There is nothing I've seen in the rules requiring A1 to keep any specific body orientation as they move around the court. The rules requiring the arms, hips, legs, etc. to remain in the frame of the torso all have to do with guarding and screening....and A1 isn't doing either (usually).

Not true. The legal moving screen must be in the same path and direction and the player behind must stop if the player in front stops or slows. Your example is in the same direction but not the same path and B1 is not in front of A1. Not applicable at all.

Plus, B1 isn't setting a screen, B1 is guarding.

Additionally, defenders never have the right to a path relative to the ball handler. They have a right to a path only when being screened and the screen is late or moving. The only path that matters in situations involving a dribbler is the dribbler's path (unless the dribbler is setting a screen).

If the dribbler cuts off a defender's established path, isn't he by definition setting a moving screen?

If a defender runs into a dribbler, isn't he, by definition, committing a block/push/charge?

Basically, you have two players that are moving such that their paths intersect. At least one of the two has the right to be moving at that time (sometimes both, but not in this case).

To determine which, you have to decide if A1 is screening or B1 is guarding.

Who is trying to get to where? Where is the defender trying go? Who is he trying to guard? Usually, the defender is attempting to guard the player with the ball. If it were a screen, who is the screen set for, who is it freeing up?

If A1 is trying to cut to the basket or otherwise make a play with B1 is trying to stop A1, this simply can not be a screen, it is a guarding situation. B1 must have LGP at the time of contact in order to be moving legally.

If B1 is trying to get to another player in order to guard them (perhaps a pick-and-roll type of play where B1 is trying to cover the roller), A1 must set a legal screen....with time and distance.

In the situation as presented, there is no indication that B1 was doing anything other than trying to stay with and guard A1. Thus, B1 is guarding (poorly) and A1 is not screening....guarding rules apply. During a guarding situation, the only path that matters is that of the offense...the defense must get in the spot before the offense. If they're running side by side, I don't see that the defender beat the player to any spot, the defender was late. Even if the dribbler did a perfect 90 turn toward the defender, the defender was moving and was never facing the dribbler...still a block.