"Knowledge" on its own tends to be specific: "Did you have knowledge of this relationship?". The kind of knowledge referred to in examples 3, 4, and 5 is specific, though not as specific as in my example. Incidentally, I think there's a typo in the example: it's most probably "MI5" (a government department that deals with Military Intelligence.)
This leaves 2, where I'd have expected to see a. But as it's a specific addition to her general suitability, the omission is fine. She was hired, say, because she had a knowledge of German and Russian; the fact that she can handle francophone customers when required is a specific bonus.
(As many of these examples show, the distinction I'm aware of as a native speaker is not hard and fast. Other teachers might hold that there's a more simple equivalence of the two versions.)
Student or Learner