missed questions

Can someone provide some clarification on these questions:

1) After the ball becomes live to start the game the scorer signals the referee to the table. The scorer notifies the referee that No. 24 started instead of designated starter No. 23. Referee assesses team A with a technical foul. Is the official correct?

I answered yes, but the correct answer was no. my assumption is the reason my answer was incorrect is based on the issue being detected after the ball became live. However, I cannot find this in the rulebook. Is this covered anywhere other than 3-2-2 and 10-1-2?

2) A-1 catches the ball while in the air. A-1 lands on one foot, jumps off that foot and lands simultaneously on both feet. A-1 then lifts one foot off the floor and starts a dribble. Official rules this a legal play. Is the official correct?

I answered no, but the answer was yes. My understanding is that neither foot can be the pivot and he must pass or shoot once he lifts either foot off the floor. Lifting the foot to start a dribble should be an automatic travel, correct?

3) A-2 in the frontcourt bats A-1's throw-in into the backcourt. A-2 retrieves the ball in the backcourt. Official rules this a legal play. Is the official correct?

I answered no but the correct answer was yes. Another typo or am I missing something here?

4) A-1, while dribbling, intentionally pushes B-1. Official rules this a player control foul. Is the official correct?

I found this one confusing. I answered yes, even though I knew it was an intentional foul. However, is it not still considered a player control foul, or is it simply an intentional foul?