-Why does Leonard thank the policeman?

Because he didn phone the cops. 

-What's wrong with the son of the policeman's sister  ?

That he is special.

-How does Leonard call  Sheldon when he enters the ball pit?

Shelly. 

-What does  sheldon tell leonard when he's entering the pool balls?

That he can try, but he will no be able to catch him.

-What is the word that Sheldon says when Leonard tries to catch him?

Bazinga!
-How often does he repeat it?
each time Leonard goes to the spot where he last was.