In Detective Comics #6 & #7 a group of five (I think) villains (I assume) are shown as keeping their valuables in the Penguin's vaults. Two of them are referred to in the comic that I can see:
Who are the other three? Have they been encountered before?
These are (as described in numerous reviews/Wikias) "second-string villains" who wanted to invest money with Penguin to avoid being killed.
3 of them can be identified with certainty (standing ones); and one can be identified but not 100% certain:
Hypnotic (identified by hypnotic spirals in his eyeglasses, and bandanna on his mouth)
Mr. Toxic (aka Gas Man)
They are identified by name in the following 2 panels in Detective Comics #6:
One more villain sometimes listed in their company is "Imperceptible Man". He COULD possibly be the guy holding Jill, but I'm skeptical.
Reasons to think that guy is NOT "Imperceptible Man":
His images elsewhere in the comic (where he is dressed and 100% body-invisible) don't seem to match the picture above.
vs. 
Reasons to think that guy is indeed "Imperceptible Man":
The wispy gas-like-translucence could possibly be the artist's way of drawing "Jill got caught by invisible person". If he wasn't drawn that way, we would see her being "held" by empty air - impossible to depict.
Jill is a good martial artist. If she WAS caught by anyone, an invisible guy would be a likely candidate as he could take her by surprise.
Note that the guy is drawn naked. Is there a possible reason to draw a male mook as naked unless it's because he's really invisible and thus being naked would have helped him in sneaking up on Jill?
We see the other 4 guys PLUS the Imperceptible Man (with a matching "100% transparent" pic) together elsewhere in the comic (Det.C. #6 page 1 - shown above; and ALSO D.C. #16 and D.C. #19 - the latter is when he is actually named for the first time).
D.C. #6 page 1 is right before Jill is caught - they likely wouldn't change the 5th member of the thug party that quickly to yet another mook - ONLY to replace him back with original member after that 1 short.
Also, Mr Imperceptible is listed together with Hypnotic/Toxic/Combustible elsewhere in many issues; and there's no mention EVER of a "guy that looks like a gas-traslucent-Genie". So the pattern seems to indicate that Mr Imperceptible is also a part of the gang in the OP's page.
The last guy wearing the armor on his head isn't identified at all. Ever. In any DC comic up to #19.
I checked the names of all characters listed in various sources and he ain't one of them ([Batman Wikia], [ComicVine], [DC Wikia], and Comicvine for "Faces of Death" and re-read DC. Comics #6,7, 16 and 19 which are the only ones containing the other 3 mooks.
The other villains listed on Wikia don't match: Mr. Mosaic has a different look, Snakeskin isn't part of "investors" and was injured in prior scene to the one being asked about by exploding gun Jill gave him; Chase/Lark/Trina are women; Smitty was Pog's flunky that Batman interrogated in #6; and not one of investors; Louis Hill was also a different character Batman interacted with; "George Weaver" was just a disguise for Snakeskin.
To answer your separate question, both ComicVine character pages and Batman Wikia list the first appearance for all 4 of the named ones as Detective Comics #6.
