Some good questions.
One view is that if there is change, there is time. However, it doesn't follow from that that time has a "metric" -- that there is an answer to questions of the sort "how much time?" If all that existed were two solid spheres in relative motion, then someone might say that there's no answer to the question "What's the relative velocity?" (hence how much time has passed between varying degrees of separation) even though there is change going on, and hence there's time.
More generally we can at least imagine a universe where time _order_ among events -- what happens before, after or simultaneously with what -- is definite, but without there being any correct answers to questions such as "How much time passed between event x and event y?" Insofar as that's right, it provides a way around your objection.
Whether time requires change is yet another question. Not everyone agrees that it does. Sidney Shoemaker, in a paper from some years ago, argues that there could be definite periods of time with no change. The reference is: “Time Without Change,” Journal of Philosophy 66 (1969), pp. 363-381. You might also look at the article on time in the Stanford Encyclopedia of Philosophy:
Good luck with your explorations!