And also, and excessive focus on unit testing inhibits refactoring.
Not in my experience.
What if I split C into two or more classes?
So C was too large and now you're fixing it, splitting it into C and CPrime. Great! Good unit tests for C insure this refactoring doesn't break desired behaviors. If a test fails, it's doing its job, warning you that you did part of the refactoring wrong. Because unit tests are closer to code they test than integration tests, it will be easier to locate the problem and fix it.
Do I have to rework and split all its tests, so that they'll be one-class unit tests on the new classes?
No. If you do refactorings in small steps as described in Martin Fowler's book, the tests don't change (except for name and signature changes that I hope you are using a refactoring tool to do.) CPrime is indirectly tested by the tests for C.
AFTER I've split the class, and the tests are still passing, I may move some tests to directly test CPrime.
Further refactorings might remove some of the forwarding-functions from C that you would have created if you were doing the Extract Class/Move Method refactorings as per Fowler.
What if I decide to combine C and D into a single class. What will that do to my tests?
You change change all users of C and D appropriately, whether those users are tests or production code. Refactoring tools make that easy.
Avoiding the code smell "Duplicated Code" in both your test code and your production code insures that all the changes required for a Merge Class Refactoring are minimal.
And how will my tests help me determine if the new combined class is correct? If I have only unit tests for C and D, then really I won't have any way to determine if the new combined "CD" class is working correctly?
There are three activities in TDD: (1) writing a test (usually one that fails first), (2) writing code to pass a test, (3) refactoring to clean up code smells.
By separating #3 from #2, you are much less likely to have problems. You do need new skills: refactoring is not the same as "rewriting"; you can't let code smells go unfixed for very long; and you need to know how (and when) to use fakes and mocks to test how objects collaborate and also break dependencies to test in isolation.
Because tests in TDD _do_ allow collaboration between multiple objects, they might not fit your definition of a "unit test". That's one reason we at Industrial Logic call them "microtests". Each microtest only tests a single behavior, setting up the class under test with real or fake collaborators as needed.
You might find IL's courses athttp://elearning.industriallogic.com/gh helpful for learning Refactoring, Code Smells, TDD, etc.
Hope this helps,
C Keith Ray