can you convert a png to vector?

Use the camera icon to attach the image.

In the Live Trace Options pick select your preset or make custom settings including color.

Tat wow answer you go tis nothing more then a misunderstanding of how to use the live trace feature.

It really depends on what your point of view is and true the settings are difficult to understand and require a lot of experience to make work well but the standard tracing will give you  good results.

One thing I want to point so you understand the the wow answer is way off track and that is that it is call LIve Trace because it is not converting anything to vector it is not intended convert anything to vector does not say or imply it converts raster images to vector art as it is only a tracing feature for creating vector art based on a raster image.

This might help you see it from another point of view that does not have issues to confuse the matter.

http://graphicssoft.about.com/od/illustrator/ss/sflivetrace.htm

and this

http://www.adobe.com/products/illustrator/pdfs/creating_vector_content.pdf

Note that hough the word conversion is used it does not imply the same notion as the wow answer suggest it implies, it simply means you are using a raster image as a basis for creating  vector form of that raster art.

Nothing more and nothing less.

BTW the straight forward answer to your questions are contained in the two above links.