The situations that I had when officiating a game was, A girl was shooting a free throw, she took two dribbles and the ball went off her knee, my partner called a violation, is this a violation or not.

Common sense, give her the ball back...

Case book 9.1, give her the ball back. Common sense and rules both say partner was wrong.

9.1 SITUATION: A1, at the free throw line to attempt a free throw (a) muffs the pass from the official and it rolls forward; or (b) accidentally drops the ball before the throwing motion is started. Ruling: In (a) and (b) the official should sound the whistle to prevent any violations and then start the free throw procedure again.

No, not a violation. Blow the whistle and get the ball back to her. Now, some might say if she steps out to go for the ball then you can have a violation. Yes, this would be a violation. Thats why you want to have a quick whistle to stop play, then if something goofy happens there is no violation.

Okay, give the ball back, but here's the tough one -- does she get another 10-count?

Did you think the muffing the ball off her knee was an intentional delay? Like the player that spends 10 seconds to shoot a free throw? I'm thinking not.

Start over from the beginning with a full 10.

Getting to 10 seconds on a normal free throw is nearly impossible because, when we get to 9, we start counting by fractions.
mick

So she gets the same kind of ten count she would have gotten anyway ;)