Caveats of punctuation of nested quotes

I've found "How to punctuate a quote within a quote?" where the correct punctuation for the given example of nested quotes was:

“He leaned close to me, and said in a gravely and drunken voice, ‘It’s not easy.’”

This shows the obvious point of not doubling the full stop, and having it contracted to the end of the sentence inside the quote.

The question has been closed despite dealing with a matter not answered in any linked to questions (they were either about punctuation within normal quotes or about double quoting but not about both at the same time) - though I understand it might be thought to be obvious if the intuitive combination is the correct one. Unfortunately in my case I really suspect "intuitive" is incorrect.

"It’s not easy" is a sentence and so, a full stop comes at its end naturally. Now, is the same rule true if we use quotation marks for other purposes?

Is the below correct?

“Why should I ever hear about this... ‘agency?’”

‘agency’ is quoted for being an euphemism here. Normally the quote mark belongs to the outer question. Is pulling it inside ‘’ correct or should it go between ’ and ”?

Next, comes a matter of how to contract multiple conflicting ending punctuation marks. The below example is most likely incorrect, but how would one properly punctuate:

He screwed his eyebrows, and asked, "Are you sure you heard 'Stop!'?".

If the various quote levels contain sentences that require different punctuation at respective ends, how does one reconcile them?

Answer

In your first query, the question mark clearly does not belong to the euphemism, so it should not appear inside its quotes:

“Why should I ever hear about this... ‘agency’?”

In your second query, you can dispense with the exclamation mark. While that does go with the word Stop, it isn’t heard and doesn’t need to be quoted. And the final full stop isn’t needed either — you’ve already conceded that right at the start.

He screwed his eyebrows, and asked, “Are you sure you heard ‘Stop’?”

Punctuation is only there to assist understanding. Too much clouds the meaning because although it might be strictly correct, it requires working out! Use enough to make the meaning clear without undue effort sorting through it all.