Question

Do stars revolve around the center of a galaxy in a preordained path, like planets do around stars?

Answer 1

Yes. Our star Sun and its system of orbiters revolve around Milky Way center.

Explanation:

It is a scientific estimate that the Sun revolves about about Milky Way center with period about a quarter of a billion years.
Sun;s distance from the center is about 63 K light years.