On the opening jump, A1 and B1 both tap the ball. The ball stays in the circle and B1 taps it again. I know he cannot catch it until touched by a non-jumper. Can he tap it again, though?

If the ball hasn't hit the floor, the backboard or a non-jumper - no. If it has done at least one of those things - yes.

Each jumper can tap it twice even before it hits anything or anyone else.

Once it has done at least one of those things, the restrictions are off and the jumper can even grab the ball.

Help me out here.

This happen at one of my game. Partner hit the whistle did a little tap signal and pointed for a blue spot throw in. Arrow got set to white.

Correct? If not, what is the correct signal.

There is no specific signal. Hand up, whistle. Point to the center circle. "Violation, blue ball" "Set the arrow to white" Much like a free throw violation or a throw-in violation.

Each jumper can touch the ball no more than twice, until after it hits the floor, a non-jumper, the backboard, or the basket. (6-3-7) So if your partner called a violation for a second tap, he missed it.