>Why the fuck did he find the need to go back to his house before the rooster crowed three times?
You answered this question on your own—he was highly suspicious of her. She's telling him something terrible will happen to his family unless he listens to her, but he's already been burned by the old man, quasi-zombies, a hack shaman, and the ineptitude of the police force. His daughter is suffering from a possession/sickness and his family is in splinters. It's a paternal instinct to try to physically convene with one's family in a dangerous setting, especially if the alternative is waiting for a rooster to crow three times. I agree the setup is absurd in itself (though not in a negative way, as such a tone is typical of Korean supernatural movies), but I don't think his action was necessarily irrational. I do agree, however, that the tragedy of the ending was both contrived and predictable.
>Nobody decides to detain the Japanese man as a suspect?
Didn't the man run away? It's been a few months since I've seen the movie, so I'm not positive.
>And the girl is able to go back home after stabbing a woman with a pair of scissors?
It's a small village. No one is going to sue a little girl for having a freakout episode. I guess they could've put her in a ward or something, but how would that change the movie? She'd still be possessed and slowly deteriorating in her humanity.
>And the "zombies" attack officers and nobody tries to restrain them? They are never put in handcuffs?
They were definitely restrained through brute force. Good point about the handcuffs, though. I imagine it was a bizarre form of humor; Korean filmmakers are known for abrupt tonal shifts.
>The first guy who murdered two people was allowed to just sit on the porch with no restraints whatsoever?
I imagine you understand how minor this gripe is. It was for dramatic effect. In real life, yes, he'd have cuffs on at the very least, but come on, he was clearly shown to be an empty shell.