What you are feeling and seeing might be remaining binder from the paint itself, it could possibly be thinned with a solvent, or a good scrubbing since Acrylic uses a water base rather than an oil. The chalky look and feel is the result of a matte finish that Acrylic creates. Some acrylics can be purchased in glossy finishes, but a lot of the guys around here recommend Testors or other types of model paint. I assume that some of them go on with a smooth glossy finish.
To prevent chipping, which will occur with any acrylic paint, and most paint in general, you need to clear coat it, using a varnish like Krylon's crystal clear, which is a transparent varnish that gives a glossy look. Some spray paints are another option for nice base coats, but obviously will not work for fine details.
Hope this helps and good luck
br()wnie