I mean-- technically? You can establish some resemblance of a friendship, but you won't truly be friends. You might be able to tolerate them, minus the things you've mentioned, but overall? Their jealousy, possessiveness and lack of understanding/refusal to accept not only where they stand in your life but also how they're in the wrong and their refusal to handle things as an adult will only cause resentment, irritation and a negative impact on you.
There's a difference between being cordial and being civil. I would suggest the latter. Be civil with her, as you both work together, but just because you treat her with a basic respect and human decency, doesn't by any means or stretch make you friends nor do you owe her any sort of explanation or communication that doesn't pertain to your jobs. You don't have to be friends.
I mean, it's clear you've tried. She's not getting it and doesn't want to change-- She apparently sees nothing wrong with her behaviour and it sounds like you've tried to lead the horse to water there. You can lead a horse to water, but you can't make it drink. You can set the boundaries and advise her on how to proceed and explain until you're blue in the face, but if she wants to reject it all and keep with her current ways, that's what she's going to do.
At some point, you need to determine when it's just simply not worth it and prioritize yourself/your boundaries/your right to maintain as little her related stress and irritation as possible.
How old is she? She's acting like a very young and immature person. While age doesn't exactly define how people will act-- anomalies exist all the time with people acting younger or older than they truly are-- it's still a good measurement gauge of what one can expect. Pleasant surprises do exist, but it's better to be prepared.
As far as confrontation goes, it sounds like you've had this discussion and explained to her several times that her behaviour is unacceptable. What good is another talk going to do? I would tell her, straight forward but maintaining professionalism, that you're done with her garbage. She either realizes you don't want to be with her in the slightest and stops acting like a child with her tantrums as well as knocks off the controlling/possessive and jealous behaviour or she loses you all together and you will strictly be work only. "Do not talk to me if it doesn't pertain to the job"
Yes. That's an ultimatum, but sometimes? Those are necessary for your own boundaries.
