no, one eye can have astigmatism and the other just have a spherical prescription. for example, OD(right eye) could be -1.00 -0.50 x 90-astigmatism part of the rx and OS(left eye) -1.25.
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Yes. These two ocular conditions have two different causes. We have myopia due to the fact that our eyeballs are too long (in axial length) in relation to how steep our corneas are.
Astigmatism is usually caused by the fact that our corneas are not perfectly round (spherical). Because of this, light is not focused clearly on one point on our retina.