Council of Elrond

Okay, if I play Incite Denizens

Creates an additional automatic-attack at a Ruins & Lairs [R] until the end of the turn. This is an exact duplicate (including all existing and eventual modifications to prowess, etc.) of an existing automatic-attack of your choice at the site. This automatic-attack is faced after the automatic-attack it duplicates.
Cannot be duplicated on a given site.

on an At Home attack, and the At Home attack is defeated, what happens to the attack created by Incite Denizens? Must it still be faced, or does it vanish in a puff of common sense?

After the At Home's defeat, the site no longer contains automatic attacks, which constitutes an 'eventual modification' and therefore, as my father would say, twice nothing is nothing.

Or from another angle, the fact that the site no longer contains automatic attacks, the attack created by the Incite Denizens doesn't exist anymore either, regardless of what kind it is.

A perhaps more interesting question is what does this do to other cards or effects creating automatic attacks set to be faced after an At Home dragon manifestation? Do they also disappear in a puff of 'not necessarily common sense'?

OK, so upon further review, I'm a moron.

It isn't the text of the At Home card that cancels the further auto-attacks at the Dragon Lair, however, if I'm not mistaken, there is a rule out there that says the Dragon Auto Attack is cancelled if a manifestation of the dragon that lives there is defeated, (I am right about that aren't I?) Maybe not...

I guess I go back to the "exact duplicate" which means it is a unique manifestation of the dragon, and a modification of that attack that is an "eventuallity" of the defeat of the first is that it would no longer be playable, so the second attack poofs out.

Inversely, should the dragon be eliminated if the Incite version gets killed, and what of the potential kill MPs?

I should stop smoking crack and going to work.

Bandobras question is already answered by CRF:

CRF, Errata (Cards), Incite Denizens wrote:When copying an attack put on the site by another card, Incite Denizens will not copy any other effects of the card. When copying an attack put on the site by another card, the Incite Denizens attack will disappear if the other card is discarded.

So "it [does] vanish in a puff of common sense".

P.S.
Another episode in "choice vs target" war.
Is this card playable on automatic-attack or on the site (and which AA will be copied is choosen at resolution)?
In other words: is "of your choice" meaningless or is it meaningful?