Running The Baseline Question

[Brad]

can A1 bounce the ball to A2 as long as the ball doesn't touch the end line or any part of the court in bounds?

Absolutely. There is no restriction on bounce passing the ball to your teammate.

can a player on the spot before an inbound pass dribble the ball during the five second count?

If they want to!

There is no restriction on dribbling or traveling, etc. on a throw-in since the ball is not in play on the court. The player can bounce the ball, catch it, bounce it again, dribble it, etc. -- as long as all that and the throw-in itself is done within the 5 second limitation, they're fine.