Sorry my guy but i have to disagree (no shade). I always saw PB as a batman-like character while having a mother nature towards her kingdom. Everything she has done has been either for protecting her kingdom, or to help her friends. She's helped marceline multiple times, gave fin his prosthetic arm, saved lady rainicorn when they were in danger despite the fact that lady told her to leave her, and countless other things. She definitely had her power hungry moments don't get me wrong but nothing that really indicates she's not a good guy. Like i said, she's just cold and calculating and it can come off as being bad. As for the things you said:
she doesn't care about flame princess being held captive because the candy kingdom and fire kingdom are two separate kingdoms and have their own rules and customs. PB is royalty but she has no right or reason to interfere with the affairs of another kingdom so naturally she isn't gonna try to save her. And she asks her dad to contain her because she was burning everything and could have killed someone.
The duke of nuts thing was meant to be comedic lol but maybe she was being a bit too aggressive
I sincerely can't remember a time where she "manipulates" fin. I think its more of a thing where he was in love with her so he did whatever she said voluntarily. Besides she never put him in a situation that threatens his life as far as i can remember.
When PB saw how goliad was too far gone she had to make her stop using stormo. Otherwise she would have hurt someone. I really don't get why you see that as anything but good.
The king of Ooo was a horrible ruler and he deserved to be usurped. Regardless of how.
I never saw her to be bad or even neutral. She was always good person. She just didn't know how to obtain her goal without being cold and sometimes she did take things too far.
Again no shade. This is my all opinions and i just wanted to say what I thought of her.