How much can a child earn and still be claimed as a dependent?

A child aged under 16, can not be paid minimum wage or more.

Also a child under 16 can not work in a full time or part time job, or a job that causes risk to their health, and they can not work instead of go to school.

The only jobs children can do are things like paper-rounds, baby sitting, car washing ect.

Wrong. See here:

http://ezinearticles.com/?Using-an-All-in-the-Family-Business-to-Get-Tax-Breaks&id=2152109

As of 2008 that amount was $5150/yr.