I explain it much more in depth in this post at fandom_grammar. I am American taught, so some discrepancies may exist, however, the ellipsis is more precisely an omission. Fiction uses it a bit more liberally and that's why it's in good form to use it as a pause—in fiction. I would never use it as a pause in a research essay.

If the ellipses came at the end of a sentence, it was necessary to include a period, something no one seems to do these days.

This is true and is what I explained to zats_clear above.

Em dashes are for parenthetical clauses, but like parenthetical clauses that are set off by commas, you don't need a second one to "close" the clause if the sentence is ending.

Abrupt closing breaks were indicated by endashes or two hyphens.

This is something I need to research. The only time I've actually seen an en dash used is for a span like "5–10."

Also, generally it's accepted in American that 2 hyphens make an em dash and most people ignore the en dash. (Thankfully I can make them both on my computer. YAY!)

Admittedly, the exceptions are rare and the overuse lessens the effect.

The exceptions are quite rare and mostly I just want people to punctuate correctly. I think the real driving force is that people don't understand what punctuation means and why it's so important. Once they understand what their punctuation is saying, I think they'll know how to use it effectively.