- What if the player tosses the ball and catches hold of it without serving as that of lawn tennis where it usually happens?
- What if the ball falls down without contacting the bat after tossing?
For question one, where the server throws the ball up to serve, but changes his mind and catches the ball instead of hitting the ball - the relevant laws are:
ITTF Laws of Table Tennis
2.6.1 Service shall start with the ball resting freely on the open palm of the server's stationary free hand.
2.6.2 The server shall then project the ball near vertically upwards, without imparting spin, so that it rises at least 16cm (6.3 inches) after leaving the palm of the free hand and then falls without touching anything before being struck.
2.6.3 As the ball is falling the server shall strike it so that it touches first his court and then, after passing over or around the net assembly, touches directly the receiver's court; in doubles, the ball shall touch successively the right half court of server and receiver.
2.6.6.3 Whenever there is a clear failure to comply with the requirements for a good service, no warning shall be given and the receiver shall score a point.
As you can see from the above rules, there is no provision to allow the server throw the ball up, then catch the ball instead of striking it. So once the service has started by the server throwing the ball up, he must strike the ball as specified by Law 2.6.3. If the server catches the ball instead of hitting it, then the ball has not been struck correctly, and that is a clear failure to comply with the requirements of a good service, so the receiver gets the point, as according to Law 2.6.6.3.
In regards to your second question, where the server misses the ball when trying to hit it during the service, I've answered that elsewhere on the site - see What Happens When the Server Misses the Ball When Serving?.
