A. - the listener is expected to know that there is a dragon, whose tail was (but no longer is) golden. No information about the current colour of the dragon's tail
B. - see Lingo's explanation
C. - I agree with LingoB, but I believe the first 'the' covers the tail as well, so the second definite article is optional really (Edit: ahh, I am confused Sounds to me fine without an article, or, at least, I would not slash my wrists over its absence )
Yes, of course it can. As always, context governs which would be the better choice — but here we don't know the context!
So, without knowing what story this is part of, we're left with the nuance between definite and indefinite articles.
The dragon with a golden tail — tends to imply that he's one of several but the others have different-coloured tails The dragon with the golden tail — makes us think this is the only such dragon and he's probably rather special