In the example given by partly_warmer, I think that “who, what, why, when, why and where” is not a series of questions, but a series of relative pronouns implying subordinate clauses. Hence they are not examples of questions which do not take question marks.
UDS, one can see something to your point, however that is how that particular authority chose to interpret the sentence. Having read the whole book, I haven’t actually caught them out on anything before that I absolutely disagree with. So … maybe.
I find both these sentences acceptable:
She asked the whys of it all.
She asked the whys? of it all.
If you agree, perhaps that illustrates their point better.
Communication first, rules second.
Sorry to repeat but, how could I put it better than partly_warmer?
Didn’t their post make a lot of sense, in that they said, with some excellent examples, to use question marks in general, but if they interfere with clarity, use a period.
Of course, if you have a sentence that creates a difficult decision about a question mark or not (like my previous sentence), the best thing to do might be to rewrite the sentence to force it one way or the other. Does that make sense?
And by the way, my individual humble opinion is that you second original example ‘Well, what do you know?’ should have a question mark – the goal here is to create a bit of suspense, which a period will not do as well.
For the first example I lean towards a period, as the goal of the sentence is really to express relief by the speaker. Note that changing the sentence to ‘God knows what we would have done.’ would make it very clear that a period (or perhaps exclamation point!)is appropriate, both from a strict gramamatical as well as communications point of view.
I think they’re relative pronouns because they qualify the word “facts”. “Who”, in this context, could not represent “Who shot JR?”, because that is a question, not a fact. It could represent “the person who shot JR”.
Leaving that aside, I would not accept
“She asked the whys? of it all.”
I would reject this partly because I think “whys” here represents “the reasons why”, but more because I would never include a question mark in a sentence; it always goes at the end (with the usual exception for reported speech, of course).
If you are writing between quotes–that is, writing dialogue for a character in a work of fiction, as it seems you might be–I encourage you to do whatever you want. Use a period instead of a question mark if that sounds right to you. Inside quotes, you are attempting to replicate how that person talks, so use whatever tactics you can employ to help you.
If you’re into slightly marginal punctuation you can always use the interrobang. I can’t get the font to work on this board so picture an exclamation point superimposed on a question mark. Here’s a website with more info.