There's a villain character in the comic I write who's giving me trouble to write for as I'm not really an expert on mental problems.
A brief description of her, she was born with a mutation that gives her super powers but she was abandoned by her parents who labeled her a demon child. She's been shunned all her life and her condition further stresses her grip on reality as her powers are hard to control. As a villain, she likes to spread chaos and havoc, believing herself to be normal and that the world is what needs changing.
What kind of psychological condition might be applicable here and what kind of symptoms are there of it? How do such people talk and behave? I want to make her insanity more genuine.
I can't speak to the insanity itself, but I do know that she'd have emotional neglect and abandonment issues, and this could cause her to seek her identity in her power. Her power would shape who she is, and in turn she would shape what her power develops into. It wouldn't be so much as her powers are hard to control, it's that they control her as much as she controls them.
It sounds like you're thinking of giving her some kind of Projection--she avoids seeing her own faults by seeing the same faults in the world around her. A psychosis of some sort, maybe even a God Complex, would lead her to believe that only she can save the world--and anyone who tries to stop her is therefore The Bad Guy.
As for how they talk and behave, in the absence of particulars you get from an expert I'd say go with how YOU would talk and behave if you were in that situation and thought that way. Make it real. The best villains are the ones the audience can identify with on some level.
I have heard at least one psychologist say that someone whose what people call "insane" would be experiencing hallucinations of sorts.
Like The Joker is called insane, but really he's just crazy, there's a difference between crazy and insane.
I did see that from a History Channel Doc. about Batman so I may have bad info.
Sounds like your villain likely would have Reactive Attachment Disorder. This arises from failure to form strong attachments to primary caregivers in early childhood (often as a result of severe neglect or outright rejection), and people with this problem often have extremely inappropriate social behavior (both being overly familiar with strangers and under-familiar with people who should be close) and generally don't treat relationships they way normal people do.