Dribble Own Shot Myth
 

The shooter can retrieve his or her own airball, if the referee considers it to be a shot attempt. The release ends team control. It is not a violation for that player to start another dribble at that point. When an airborne player keeps control of an attempted shot that is blocked and is unable to release the ball and returns to the floor with it, that player has not traveled; it is a jump ball. If, in this situation, the shooter releases the ball, then this is simply a blocked shot and play continues.

I live in NY City. Engrish is our second language.

Straight out of the NFHS case book:

4.44 SITUATION B: A1 attempts a try after ending the dribble. The try does not touch the backboard, the rim or any other player. A1 runs and is able to catch the ball before it strikes the floor. Is this traveling? RULING: No. When A1 recovered his/her own try, A1 could either dribble, pass or try again. There was no team control after the ball was released on a try. (4-12; 4-41)

In a related matter, what happens when a free throw shooter's 1 and 1 attempt misses everything and ball is still in play in key area and doesn't go OOBs? Is this considered a live ball or violation?

If a FT shooter's unsuccessful attempt doesn't hit the rim it is a violation as soon as it is clear it will not contact the rim.

If his/her first attempt of the 1&1 misses everything then it is NOT live, the shooter has committed a violation and the ball is dead...