How do multiple copies of these things work? I read that once the character becomes an agenda they are no longer in play, allowing you to play another copy of them. What then happens if the character dies again? Do they go to your dead pile? Do they attach to your house again? Are they discarded (this is a stretch, but one could argue that they do attach to your house based on it's game text and then is discarded because the card is unique)? Do they attack to the agenda as a duplicate (again a stretch; I don't think the rules allow an agenda to be duped)?
All of the pieces you need exist in the FAQ and the Core Set rulebook. (Look especially at p. 12. The "(4.20) Character Agendas" entry answers some of this stuff directly.) My guess is that if you take the time and think the situation through, you'll be able to answer your own questions.
Multiple copies of the character agendas work by their text and the rules for unique cards. Since agendas are not considered "in play," then once the character is attached to your House card as an agenda, it is no longer "in play." Since it is not "in play" or in your dead pile, there is nothing stopping you from playing another copy.
If the character dies again, you look at the text - which says if it dies, it is attached to your House card as your "only agenda." Well, you already have an agenda - the first copy of the card - right? That means the play restictions for the "attach as an agenda" text are not met, so the dead character just goes to the dead pile. (Not the discard pile. Attaching as an agenda is a replacement effect. If the replacement effect is invalid, the original "goes through," which in this case means the death.)
Since agendas are "out of play" and unique cards only duplicate unique cards that are "in play," the second copy could never become a dupe on the first while it is an agenda. If you have two copies of Robb Stark in you hard or discard pile, is one a dupe in the other? Of ocurse not. It makes no more sense to "dupe" agendas.
As a follow-up to question #1, how does Griff work, specifically? If he attaches to your house, then you play another copy, and then Griff's unattach effect triggers, what happens? Does he stay attached to your house card because there is already a copy of him that you own in play? Does he attach himself as a duplicate like a duplicate coming out of Shadows would? Is he discarded?
Whenever a "put into play" effect puts a unique card into play, and you already have another copy that you both own and control in play, the second copy becomes a dupe on the first. So if the Agenda Griff would re-enter play and you have played another copy in the meantime, the copy coming into play from being your agenda becomes a dupe on the copy already in play.
How do cards that react to not having an agenda work with these? If The Kindly Man is on my house card, does Maege Mormont no longer work? Are having these character agendas considered "running agendas"?
The characters become agendas. If you have an agenda on your House card, you are "running an agenda," whether you started the game with it on your House card or not. This is in the FAQ.
What happens if these cards effects trigger while I have an agenda? Do they go to the dead pile? Do they attach to the house card and not work? Do they attach to the house card and negate the other agenda (kind of ambiguous with the "as your only agenda" wording; would have been clearer to preface the ability with "If you do not have an agenda…")? Is the result different if the agenda is an actual agenda vs. another character agenda (i.e. if you were somehow able to run both Griff and The Kindly Man in one deck)?
See the answer to #1. If you already have an agenda on your House card, then the "as your only agenda" text on the character-agenda is not valid, so the replacement never happens. If the replacement effect never happens, you killed character goes to the dead pile. This is in the FAQ.
Another question about Griff specifically. How does his timing work within a particular framework action? Or rather, when does his "put back into play" effect actually resolve within the framework window? Does it happen within the window of the action that killed him or is it the first thing that happens within the next window? When would you be able to respond to him coming into play (or can you respond to it at all)?
His "put back into play" text triggered when you physically
have fewer attachments. If you get to such a count because opponents play
additional attachments, it will happen (passively) in the same window in which the extra attachments came into play. But if you get to such a count because your attachments are discarded
, the fact that they remain on the table in moribund means that Griff will not actually come into play until the (first) passive step of the next
Are you able to use cards like Retreat on these characters? I am not sure why you would want to, but the main part of the question is when does the replacement effect occur; when they are killed or when they leave play?
The replacement effects happen when the original killing effect resolves. So they go into the "moribund:agenda" state rather than the "moribund:dead pile" state. But they still count as being killed (otherwise, you couldn't satisfy claim with them), so that's what you can Respond to. So you could use Retreat's "after a unique character is killed" Response to change the "moribund:agenda" state to "moribund:hand" if you wanted to.