A player has stopped her dribble and passes to a teammate, that is not ready and so the passer goes and retrieves her own pass.

A player has not dribbled and does the same thing.

Can someone give me some thoughts on this?

I do not believe you can pass to yorself

If the player has NOT dribbled they may retrieve the ball, and continue dribbling or gather it. If they gather they may not dribble again.

If they had already dribbled, it becomes an illegal dribble when they touch the ball again without it touching another player.

The rules on starting a dribble allow a player to throw or push the ball to the floor, so this "pass" becomes an interrupted dribble when the teammate fails to catch it.

So, if the player has used their dribble, passes the ball to a teammate and then goes to get it by grabbing the ball. Is the v. call in this case traveling or ddribble?

Illegal dribble.

The violation is for an illegal second dribble. You cannot travel while dribbling, by rule.

Situation: A1 is holding the ball, throws the ball, then retrieves the ball before anyone else touches it.

If the ball does not bounce before A1 retrieves the ball, we have a traveling violation.

If A1 has already dribbled and the ball bounces before A1 retrieves the ball, we have a double dribble.

If A1 has not dribbled and the ball bounces before A1 retrieves the ball, then this is a legal play---the beginning of A1's dribble as blindzebra said.

Actually, it used to be a travel in that first case, they changed it to an illegal dribble 4.15.4.E

Is this true under NCAA rules as well? I just spent a while looking through the book and couldn't find it anywhere.

I'm not sure about NCAA, but it was a travel before and it's since been changed to an illegal dribble, and in either case it's a violation so it's not a big deal what signal you give, the act is still illegal.