我不明白

When to use: 理解， 明白 和懂？

Does: 我不明白 mean I don't understand and 我不懂 mean I don't know?

Completely agree with Ruosen.

As for the difference between 懂 明白 理解, for me it is the difference of how often it is used in everyday language---懂>明白>理解, but it is just the general sense. Personally speaking, I use the three words in different occasions.

Here are my personal understanding:

理解 is more used regarding an academic problem.

明白 is more general, both academis problem or social, interpersonal thing.

懂 is more close to 明白

Which to use also depends on how the question is put.

你知道这题怎么解了吗？ 我知道了（here 知道 can also mean "understand"）

你懂了吗？我懂了

---他这人就是这样，你别在意。（He just acted that way, don't care about him）---我明白(I won't/ I understand)

You need to search for more examples of real life sentences to understand the slight differences between these three words. But of course, people will understand you if you use any of it.

我不明白

When to use: 理解， 明白 和懂？

Does: 我不明白 mean I don't understand and 我不懂 mean I don't know?

It's like in English, what's the difference between comprehend and understand?  Rather than repeating, here's an English link for you.

http://www.thinkingchinese.com/index.php?page_id=95

If you can read this Chinese article...

越来越明白却越来越不懂

http://www.wenzhangwu.com/a/2011-07-30/8943.html

我不明白

When to use: 理解， 明白 和懂？

Does: 我不明白 /我不懂/我不理解 mean I don't understand and 我不懂我不知道 mean I don't know?