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1) Does Maya understand splines? or just Nurbs. If there is a way to make just usual spline, then how to do so?
A NURBS curve IS a spline. So yes you can. Nurbs stands for Non uniform B spline, so while NURBS can describe all possible other spline types exactly beziers cant explain all nurbs curves, without a lot of extra points.
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2) Does anybody know how Maya makes Bezier curves?
If split up a curve at each span you get a bezierspline, also if you adjust the parametrisation of a existing curve so that the multiplicity is varying so that each span is independent of next you get a bezierspline
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but what I need is to find out what coefficient Maya is using
That is exactly the point of Nurbs to be able to set the coefficient yourself, for each point.
You trying to export into ai eps or something? Ive done that you know. Anyway care to tell us what you want to achieve theres most likely a very much faster way to do so.