Please give us a complete sentence in which you think you might use these words. It will help people think of ways they are difference and to give you an accurate answer. (We require a sentence with every question.)
Added: Wordsmyth said the same thing while I was answering the phone.
For example I want to say that the test was difficult (not very much). So I will say ''it was quite difficult'' or ''it was a little bit difficult''
Also I want to say that I speak German not very well. Could I say that ''I speak German a little bit''?
"The test was quite difficult" suggests that it was difficult to a significant degree, though it could have been more difficult. To me, that says that it's more than "a little bit" difficult.
In the same way "I speak German quite well" would mean that your German is fairly advanced, but not excellent. (Actually, someone with excellent German might say that anyway, through modesty!). So in your case, "a little bit" is appropriate.
Note that "a little bit" is fairly colloquial. You could drop the "bit", and say "I speak German a little", or "I speak a little German".
"Quite difficult" would mean to me that the test was very difficult. If it presented just a small amount of difficulty, almost none, I'd say that it was "not very difficult" (or perhaps "fairly easy").
As to a language: "I speak German a little bit" (we'd more likely say, "I speak only a little German") would suggest to me that you know only a few words of German. If I spoke German but not well, I think I'd say exactly that: "I speak German, but not very well."
And that's the problem with "quite". As I said in #2, it's variable in its meaning.
In the context of a test, on a scale of ten where 0 is extremely easy, 5 is average, and 10 is extremely difficult, I would put "quite difficult' around 7, whereas I'd put "very difficult" at 9. But that's just my feel for it. Parla's seems a little different, but there's no right and wrong in this. Moral: don't use "quite" if you want to express something precisely.
Flower90, I strongly recommend that you read the thread that Loob linked. It shows how complex the topic is, but on the other hand you could learn quite a lot
(that's "quite a lot" where "quite" is pretty high on my scale! ).