A: The Keepers in Cthulhu Fluxx that have special powers (meaning there is some ability which could be impaired) include:

The Dreamer (cure Nightmares anywhere on the table, whether attached or not)
The Reanimator (steal The Body, if in play)
The Socialite (steal The Poet, if in play)
The Sanitarium (cure Nightmares or Madness if attached to your Keepers)
The Elder Sign (hide, i.e. neutralize any one unattached Creeper)
The Necronomicon (move any Creeper from player to player, then put the Necronomicon back in your hand)
The Ghoul (discard The Body, if it is in front of you)
The Cultist (win if in play when The Dunwich Horror Ungoal causes everyone else to lose)

Here is a flavor-text interpretation:

Regarding Madness (which only affects Investigators)
The Dreamer, Reanimator and Socialite can’t do any of that nifty stuff they do if they have gone Insane. Easy. Remember that Nightmares, however, don’t impair the Keeper, so The Dreamer can still get rid of them, even if he’s the one who has them.

Regarding Metamorphosis (which can attach to ANY Keeper)
If a Keeper starts to Metamorphose, it just can’t function the way it should. A Metamorphosed Sanitarium probably isn’t going to cure your Madness or your Nightmares (in fact, it will probably make them worse) and neither will a Metamorphosed Dreamer. The Socialite just isn’t going to be particularly attractive to The Poet once she starts turning into a frog-person.

There are some other theming issues that are raised with Metamorphosis, however, because it is so far-reaching (attaches to any Keeper).

For example, does it really make sense that Wilbur Whately wouldn’t win if The Dunwich Horror occurred, just because he was Metamorphosed? I thought a main quality of this personage was that he was pretty darn metamorphosed to begin with. Also, somehow I thought a Metamorphosed Ghoul would still eat Dead Bodies.

I consulted Andy on this, however, and he had to conclude that, while it does not necessarily make the best thematic sense, the rule with regards to gameplay, is quite clear: those special abilities are lost if that Keeper is Metamorphosed. Maybe they start morphing into something NICER than they were before!

Ghoul: “My tummy feels funny! That Dead Body just doesn’t look that appetizing anymore…”

Wilbur: “OMG where are my abdominal tentacles?! Dad’s* totally not going to recognize me without them! I am SO toast…”

* For those less familiar with The Dunwich Horror, Wilbur Whately is the abomination of a son resulting from a human woman bearing the child of an Elder God. Wilbur is trying to summon his father, Yog Sothoth, to the Earthly plane.