I cannot imagine that anybody would have a fixed strategy, since we learn new things all the time. So I would expect the Strategy to change too. So yes, it develops. A Strategy starts small. From the start to the finish of a test project or testing a release or even a user story, we start small. How to develop (and decide about) a Strategy is described in question 1.
So a Test Strategy evolves, it grows while we learn & discover more about the product. Based on risks we decide what to test first. For those areas we have more details in the Test Strategy. We go from global to more details. Your Test Strategy is “complete” at the end of your testing.