Is it ever acceptable for a period to come after a quote at the end of a sentence?

Punctuation inside quotes is a rule that was invented by American publishers and is not necessarily followed elsewhere. The original reason had to do with typesetting mechanics and is obsolete. Also, if you're preparing technical texts such as about computer programming, this can result in technically incorrect material. In practice, you are at the mercy of whoever is editing or grading your material. But to answer your question, it can certainly be "acceptable" in many parts.

Yes. See the Economist style guide:

If the quotation does not include any punctuation, the closing inverted commas should precede any punctuation marks that the sentence requires.

More at the Guardian style guide.

Actually, Wikipedia seems to give a good answer to this. I think it can be summarized as "most people just make it up as they go." http://en.wikipedia.org/wiki/Quotation_marks#Typographical_considerations

If you're an American, periods or commas almost always go inside the quotation marks. If you're British, periods and commas only go inside if they're part of the actual quote. Unless you're a journalist, or publishing fiction. Then you do it the American way!

I really don't consider one way more correct than another. I guess it just depends on what your audience expects.

The only thing that goes inside quotation marks is the quotation. If the quotation contains punctuation, the punctuation should be included inside the quotation marks. If not, the punctuation is perfectly fine outside the quotation marks.