Septet K
Stone
Secret
Prison
Fire
Order
Prince
Hallow
I wish to slightly modify my answer:
Replace aluminum pan with tin pan, and those are the 7 metals of antiquity
Harry Potter
Septet L
Egyptian Condom
Good Fortune
Gun Cartridge
Isolated Dictator
Mouth Organ
Nonsense Notions
Striking Quartz
SEPTET F!!!
Bang! Abandoning flesh orgy = Hanging Gardens of Babylon
Do my gaps petrify? = Pyramids of Egypt
Fat lips meet more = Temple of Artemis
Host chooses for duels = Colossus of Rhodes
Oh alas! Cult amasses uranium = Mausoleum at Halicarnassus
Palest outfit amazes you = Statue of Zeus at Olympia
Pros dare a final hoax = Pharos of Alexandria
Seven wonders of the ancient world
Curses! I had been trying a few of those but obviously not with the exact words & combos necessary. :mad: Well done. :smack: 
bump
Yeah, I’m still workin’ on 'em.
Here is one avenue I am exploring for
Septet L
According to a web search, the best Egyptian condom is “ChaCha”. A gun cartridge is a “round”. Both of those are kinds of dances. But I don’t know what kind of group would comprise 7 dances…
And as for
Septet I
Given the hint, it is suspicious that all the clues are two-word proper nouns. It is reasonable to assume that the words are also two-word phrases or proper nouns. However, I have not found an adequate 2-word and/or proper noun dictionary.
These are driving me crazy. Also, I am trying to work up another Septet for y’all to work on 
!
Definitely on the wrong track with L, Karen. I guess if I were to give a hint, it would be: Alias
I’m also trying Septet K with no luck.
Septet I was really too hard. Here’s a hint: There is a seven-letter word, starting and ending with ‘S’, such that if I type it into Google Search:
“Seven S*****s”
the elements of Septet I are the fourth such set to appear, by Google’s rankings.
Rather than post a bigger hint, I’ll post a bigger puzzle: What are the other septets that show up in Google when I type
“Seven S*****s”
Hint: one of these other “S*****s” septets is seven institutions, one of which is an anagram of Look, money hut!
Septet H was not fully solved; what is the “famous septet” called?
Here’s a Hint for that: Also “Seven Ss", though a different Ss” than for Septet I.
For septet L I think it matters that both words in each item are capitalized, but I don’t know how it matters. Also:
I thought Isolated Dictator could be ‘Napoleon’ - because they sent him to an Island (=Isola) and then to another. For Gun Cartridge, I thought Shell instead of round.
Hope it helps.
Yeah, I’ve looked through the lists of the Seven S*****s (and thanks for spoiling the puzzle I was trying to cook up!) and the fourth in ranking I find is
seven oil companies, one of which is Shell (thanks, Švejk!), which is Septet L, not I! You guys are confusing me!
But now I am off to the theatre, I’ll work on them again tonight.
PS, This is fun! 
You are very very warm on the first one (in fact, the answer is “Napoleon [blank]”, and in the general ballpark for the second–definitely in the right direction.
See Post #23
Do others “Show Spoiler”? I click there every chance I get! Still, my response to Karen gives away information so I may as well protect it.
Google’s “Seven S*****s” presentation for #1, #2, #5 are all the same septet (the only one I’d never heard of), and Septet I is listed #6. (#3, #4, and #1-2-5 are thus the “three other septets”.)
My “K” was a typo; I was trying to speak of Septet L for which perhaps …
Egyptian condom = Ramses; Mouth organ = harmonica = harmony
… but I can’t figure anything out.
I think your Google works differently than my Google…
Ah, but also:
Mouth organ = pan pipe ==> Pan, who is also a god of some kind.
(I have some time before I head off to the theatre.)
PS, I click on all the spoilers, too.
Yes, “Mouth Organ” = Harmonica.
That’s 1.5 of 7 solved (then, you need to find the connections)
Septet M:
A flame sitting girl.
Brokers a jumping spy.
Herewith, I limit a solo urn, nil oil.
How is Olive Flywheel?
Mangrove triggers a nit.
Refresh oily sky porno
Snarl, a framer grins my mum.
I hope I haven’t accidentally duplicated someone else’s.
Google does vary its results almost unpredictably (which I find annoying). In this case, I don’t think it’s cookies or other Google secrets, but just geographical switching based on ISP. I got same results with another machine, BUT a very different list when I accessed Google search through an anonymizing proxy server! In that search the septet I think I spoiled for you was #1, the one with a possible word from “Septet L” was #2, my “septet I” was #3, and the #1-2-5 septet Google is so proud of for my region (though I’d never heard of it) didn’t even make the Top 10.
Yes, I suppose I should be able to figure out what country you live in, if you keep posting Google search ranks! There is no privacy anymore, get over it. :eek:
Seven highest cities in the world, I think? Not sure what septet they fill.
ETA: D’oh, somebody already got it.