Every single one of your six sentences is perfect. Rather than ask yourself which ones are "right" or "wrong", try instead to detect the subtle differences and imagine situations when each one might be best used. Some sentences, such as #2a, are not commonly spoken. However, #2a is grammatically perfect and in some situations is a far better choice than #2b. The difference is that "what book" refers to the whole collection of books she had, whereas "the book" does not. "What book" means the same as "whatever book from among the books she had". The difference between #1a and #1b is similar. You might want to use "whatever" in #1a. I disagree with your interpretation of #3a. It does not mean "as many men as..." It means "whatever men..." "As many" speaks of quantity but "what men" does not. #3b does not mean precisely "the man". It means "the man from among the possible men". It is a small difference, but it is real. In most cases, "what man" is a better choice. Use "the man" in a situation where you are certain that one man will be induced to come.

1b, 2b and 3a are the correct ones.