I am not sure that any digital camera will totally meet your #2 and #5 requirements.

Here is what is available:

Canon - S2-IS and S3-IS
Kodak - Z612 and P712
Panasonic - FZ30 and FZ7
Sony - H2 and H5

All of the cameras are under $500.

Note: The Panasonic cameras low light performance is not as good as the other cameras.

Here are the specifications:


I did not include any DSLR (digital single lens reflex) cameras, because the cost would be into the thousands of dollars for camera and necessary lenses.