do stars have an axial rotation?

Sure. It takes about a month for the Sun to rotate. I say about, because the Sun rotates at different speeds at different latitudes. Some, like the Sun, spin slowly, and others spin quickly. You can tell the minimum rotation rate of a star by looking at how fat the spectral lines are. If they're fat, that means they're both red shifted and blue shifted depending on which side of the star you're looking at. If they're thin, then either it isn't rotating, or you're seeing the star from near one of the poles. Vega, for example, is known to be seen from Earth near one of the poles, and it's rotating rapidly.