Let's go with the common assumption that Misery is a banshee. Banshee are a type of fae, and fae are weak to iron. Misery and the rest of her family have a high iron content in their blood. They are virtually getting poisoned from the inside out! It would explain why they get sick so often: their own blood is harming them.
Recall that the first time it came up she said they had a high lead content in their blood, which is toxic to humans but not particularly conductive. The writers might have had the "fae" thing in mind when they changed it.
How can Poe be descended from Edgar Allen Poe's pet budgie?
This is Poe we're talking about. He's an egotistical boaster.
But the fact that Poe was disappearing while Paco was stuck in the present proves that they really are related.
Not necessarily, as they did mess with time travel. Maybe Paco, or one of Paco's descendants, interacts with Poe's ancestors in some way that causes him to end up in Gloomsville. Remove Paco from the equation...and that version of Poe ceases to exist.
How can Skull Boy eat when he has no internal organs?
Nothing about Skull Boy makes sense, actually. How can he move if he has no muscles? How can he speak without vocal chords? How come his eyes stay in their sockets? Heck, now can he even blink without flesh?
I always thought he was blinking with muscle, somehow. What he blinks with is the right color for muscle anyway. The rest...magic? Actually related to Misery in some way? Who knows.
Necrourgy (yes that is the proper word) which is mystical stuff that animates corpses.
How could Frank and Len each get the other a present without the other seeing?