Rule 6-4 talks about the jump ball, restrictions on the jumpers, and states that the jump ball and restrictions end when the touched ball contacts the (among other things) floor. (So, yes, A1 can pick the ball up once it touches the floor, assuming it has been tapped.)
Now, going to 4-4-4 (cool, huh?
), a ball which touches a player or an official is the same as the ball touching the floor at that individual's location. 4.4.4. states (in part) that touching the official is the same as touching the floor at the location where the official is standing.