Welcome to Gaia! ::

Pop-rock:

A genre which blends traditional pop elements into a rock base. The genre is characterized by simple song structure (typically following the traditional "Opening -> First Verse -> Chorus -> Second Verse -> Chorus -> Bridge -> Chorus" pattern, usually), catchy melodies, basic guitar and drum arrangements, and fast (sometimes aggressive) tempo.

The genre is broad, encompassing thousands of bands. The Beatles, Green Day, OK Go, The Aquabats, My Chemical Romance, Queen... just a few.

Saying that pop-rock isn't a genre is liking saying green isn't a color. Blue and yellow together become green; they don't become "blue with some yellow influences". Likewise, pop and rock together become a new genre which blends elements of both, pop-rock.

My Chemical Romance is a pop-rock band because their music encompasses virtually all of the genre's conventions, though, as a whole, they're less repetitious than most pop-rock groups (save for a few songs, of course). They also, as I mentioned, take influence from horror-punk thematically, theatrically, and (occassionally) in the intensity of vocals.

Also, I must correct you: pop is not always sweet, and rock is not always mean. The genres can have any emotional or thematic styles you can imagine.

Voltaire for example is almost pure pop in structure, and he sings about nothing but gruesome murders, necrophilia, sodomy, molestation, suicide... the darkest parts of human nature. Pop is defined by it's upbeat catchy melodies, not by its subject matter. Rock is defined by it's instrumental arrangements and style of guitar playing, not by it's subject matter.

Citations:
http://www.allmusic.com/cg/amg.dll?p=amg&sql=77:419
http://en.wikipedia.org/wiki/Pop-rock

No, no, and NO
Tool is rock, evanescence is rock and Rammstein is german rock, Not goth not somewhat close to goth....

Rammstein isn't krautrock (a more common term for german rock), but Rammstein isn't industrial either. They've taken influence from industrial (a branch of electronic music), but all of their work falls under various metal genres including (but not limited to) heavy metal, doom metal, and symphonic metal.

cradle of filth

iTunes also lists Aiden as goth rock. That automatically strips iTunes of all legitimacy in genre labelling.

(I know it'd be better for GilAskan to reply to this himself, but eh, my two cents)
The hardcore punk movement ended before AFI was around. Therefore, some of their music brought some of that hardcore element back. So it is a revival.

MCR isn't really that alternative. Gerard Way himself called it "pop with some horror punk influences". Personally, I just call it pop rock, rather than powerpop (which is what most bands labled scream-o tend to be)

There is a genre called symphonic metal. And the sound of Evanescence, being primarily electric guitars, shows a bit of metal influence.

And I'd more say that the early A7x was metalcore - which is, thematically, alternative fused with metal. Moreso alternative than metal, in fact. (compare the masculine nature of metal to the more effeminate metalcore, and you'll see how it's more of alternative than metal)

AFI- Meh, never heard of "hardcore-revival" just call it Post-hardcore.

MCR- Most sources call them Alternative rock including wiki and AMG. Not that kerrang is worth s**t these days, but they call them alt. rock. You can hardly call them pop for most of their material.

A7X- Most dedicated hardcore fans definitly wouldn't call them hardcore, more metalcore with strong post-hardcore influences.

Screamo is a type of Post-hardcore with different musical aspects like the vocals of it.