Understanding one another in the Fellowship

[MLD-Grounds-Keeper-Willie]

That pretty well states that he did not know Khuzdul, at least beyond the things like place names that everyone knew. He certainly did not know enough to be fluent in it.

You don't have to be taught to learn things. Besides, you can always teach yourself. And Gandalf is very old, so I assume he would have had more than enough time to figure out the language. When Gandalf says

I shall not have to call on Gimli for words of the secret dwarf-tongue that they teach to none.

it might me implying that he [Gandalf] went through the painstaking task of learning the language himself and he does not need Gimli's help. And it never said he didn't know the language.