Can you have both astigmatism and hyperopia/myopia at the same time?

Yes: Astigmatism, myopia and hyperopia are all different types of refractive error. It is entirely possible to have astigmatism by itself, or with either myopia or hyperopia.

Yes: Hyperopia and myopia refer to the length of the eye, relative to its optical power. Basically, a hyperopic eye is too short and a myopic eye is too long. Astigmatism refers to uneven optical power, which comes from the shape of the eye. If both the lens and the cornea are round, then there is no astigmatism. If either are not (kind of like a basketball vs football), then astigmatism exists.