Acrylic paint can be used on plexiglass, and lots of people have done so to great effect. For small art projects it is not generally necessary to do more than one coating. For larger projects, such as if you wanted to paint over a window, multiple coats may be appropriate.
You can use acrylic paint for plexiglas but don't plan on it staying on very well. It will most likely peel off over time unless you let it dry and then seal it with polyuerathane.
You should be able to use Acrylic Paints on Plexiglass with no problems at all. Acrylic Paint is actually recommended for use on Plexiglass for designing purposes. You don't have to worry about any chemical reactions with it, and also the designs come out looking quite nice. You can even use it as a substitute for stained glass.