We have to remember that the Americans do this sort of thing differently from us. British usage is that the full stop, question mark or exclamation mark comes INSIDE the quotation marks only if it BELONGS to the quotation; otherwise, it goes OUTSIDE them to indicate the end of the sentence as a whole.
The Yanks are happy with the following structure. Imagine a speaker asking a question about an incident...
When did President Kennedy say, "Ich bin ein Berliner?"
Note that his words were NOT a question, but they put the question mark with the words. We, on the other hand, would write...
When did President Kennedy say, "Ich bin ein Berliner"?
The mark outside recognises the fact that it is the whole sentence which is a question, not the quote.
Under no circumstances are there two full stops - or other combination - as in Sentence 1 above. Sentence 2 is OK, but I too would put a comma after 'is', as I have done after 'say' in my examples above.