No, Star, we don't do that. Both question marks and exclamation marks, as well as full stops themselves, contain a full stop. Thus, if the quote ends with a question mark, for example, that effectively ends the sentence as a whole; we do not add a further one to end the sentence itself.
Examples...
1. When I spoke to him, President Kennedy asked, "Is this Berlin?"
No full stop is then used OUTSIDE the quotation marks to indicate the sentence-end.
2. As I listened, I heard President Kennedy say, "Ich bin ein Berliner."
(As above, no second full stop.)