How much punctuation is appropriate when ending a sentence with a full-sentence quotation?

I consider the first to be the most correct, although I would precede the quote with a comma and capitalise the beginning of John's sentence.

John asked her, "Do you have the time?"

John asked her "do you have the time?" She said yes.

This is a very awkward sentence, so maybe not a good example. I would write

John asked her "Do you have the time?" She said "Yes."

I believe this is the standard way to do this.

I have never seen punctuation doubled, as in ?., in printed English.

The example given is confusing, because it uses a question mark. Let's switch to an example of "I have no homework today."

John told me, "I have no homework today." I smiled.

This seems most natural to me.

John told me, "I have no homework today". I smiled.

This looks wrong, but may be acceptable in certain circumstances.

John told me, "I have no homework today.". I smiled.

This is very wrong.

On the other hand, suppose the outer sentence is a question. Then a question mark is required, and so to avoid double-punctuating, you need to leave out the full stop from the quoted sentence:

Did I mention that John told me, "I have no homework today"?

This is correct.

Did I mention that John told me, "I have no homework today."?

This is wrong.

Your question is specific to when the outer sentence ends at the same place as the quoted sentence. The answer would be different if the outer sentence continues after the quoted sentence; in that case I believe it's correct to omit the terminal punctuation of the quoted sentence.