Am I allowed to hit the ball before it hits my side of the table?

No, volleying is not allowed in table tennis.

Do I lose a point if I serve and the ball goes off the side of my opponent's half of the table?

No, that serve is absolutely legal.

How many lets (net serves) can there be on serve?

The number of lets is unlimited. The server serves the ball until there is no let.

What happens if the ball hits the white line of the table?

Nothing. The ball is still in play.

Can you lose a game because of a bad service on a game point?

Yes, the serving rules apply for every point of the game.

In singles, can you change the direction of the ball for each of the five serves?

Yes. In singles you can serve to wherever you want.

If you still have problems concerning table tennis rules just send me an e-mail with your question.