How do I know if blade fits the miter saw?
The diameter is important, as that's the maximum size blade that will physically fit in the saw.  The arbor size is important, because that's the size hole that will fit on the saws mandrel. If either of these sizes are wrong, the blade simply will not fit on the saw.

The thickness of the blade doesn't typically matter, as far as fitting on the machine. Unless you're talking about a dado stack, but you'd not be putting that on a miter saw anyway. The blade thickness, or kerf, only tells you how much material will be removed when cutting.

The number of teeth influences the speed of the cut, as well as the smoothness of the cut.  Generally, more teeth give a smoother cut.