effecting the outcome

[Lotto]

A1 leaps in front of B1 and deflects the pass.

Clearly no control by A1 here.

A1 is the first to get to it, but because of the pressure by B1 is only able to bat the ball forward down the sideline.

Since A1 never held the ball, again no control by A1.

...but amazingly A1 is again the first to reach the ball and saves the ball by directing it diagonally forward toward her basket while tip-toeing along the sideline.

It's hard to figure out what's happening here, since "directing" the ball could mean simply tapping it forward (in which case A1 still doesn't have control and this isn't the beginning of a dribble) or sort of catching it in one hand and guiding it forward (in which case A1 obtained control and this is the beginning of a dribble).

I'll deal with both cases below, but perhaps you could tell us which of these actually happened...?

The ball bounces up into the area of her stomach and she pushes the ball back to the floor with both hands, continues running toward the basket, and when the ball rebounds from the floor she touches it with only one hand and pushes it back to the floor.

Going back to the two possibilities that I outlined just above: If A1 has not begun her dribble, this is legal and she is dribbling now. If A1 has begun her dribble, the touch with both hands ends her dribble and the following bounce and touch would be a violation.