I just got a really light, but cheap, ceramic water filter.

I don't have much experience with these.

I want to test it to see if it works properly.
Should it be able to filter out soap and food coloring?
How can I test my filter?

You need polluted water and a microscope! The filter won't filter food coloring, and soap is not advised unless you enjoy the soapy flavor in your water.

If it's one of the standard makers, such as Katadyn, you should be fine. I'd be wary of something from a cheap and little known source. Also see the info put out by the Centers for Disease Control.

As with most backpacking gear: "Light, cheap, and good - you can have two."

Glenn is right with his saying.

It might help if you state the type of filter. Maybe someone here has some experience with it.

for sure it won't remove food coloring, one of the first times I used my filter it was from a stream with alot of leaves and the filtered water looked like tea. Tasted ok but was not my preference!