Girlfriend made my facebook account?

Run away, that's all sort of concerning (What else has she done? you only found this by accident)
I think you already know to end things as you don't say a single positive thing about them.

My brother saw my account. I have never made a Facebook after I stopped using my account back when I was 17.
I'm 29 now. She is nice, seems caring but she compliments me a lot on my looks, like how she finds me super attractive. Her second topic is how the Indian population and government mistreat her community (she's dalit) and how dalits don't get any privileges and she's a bit possessive as well.

Re: Your brother. No what I mean is you only found out about the facebook thing because he saw it and told you, so what else has she done in your name? since she has some v funny ideas about boundaries.
You've went in a few mins from saying she's very possessive to saying she's only a bit possessive... but her behaviour is obviously making other people uncomfortable and should be a screaming red flag.

She posted our pic on my birthday very fast after we became friends.
Then this Facebook thing. The account only has her as the friend. Nobody else.
I don't know and I hope nothing is done.
Are these red flags?

Does she have to literally buy a red flag and stuff it down your throat before you'll understand? She's damaged & dangerous goods.

I was conflicted because a mutual said it's fine so what if she posted our picture and made my account.

Without your permission or knowledge? Well it's basically impersonation and a pretty big breach of trust. Can you describe a situation where this would be seen as wholesome and positive? as the way you describe her as very possessive and insecure makes it kinda obvious she isn't doing this to be helpful, it's about control.
What did your friend have to say about her stalking your ex and making her so concerned she had to take action to protect herself, did they say that was fine too?

I started dating this girl in December. She's an MA student from India and we met in September during freshers week. For most part she was nice and she posted our picture on her Instagram wishing me a happy birthday and thanking me for being part of her "crew" alongwith a ❤️
We started dating in November and things were alright. Until my brother texted me saying that he saw my Facebook account. I have never had a Facebook (only when I was 17 and I had deleted that one) so naturally I was a bit surprised. I searched myself and saw that my account was up alongwith a couple pic of us in the snow and she had added herself as my only friend.
I was a bit shocked to see this as I didn't expect this at all nor did I like this.
I haven't spoken to her about this but this didn't seem like a green flag to me. She is quite insecure and very possessive as well. She kinda of stalked my ex gf on Facebook, causing my ex to hide her posts and friends.
What does this mean? Should I dump her? We are both 29.

I wonder if she made your Facebook for 1 of 2 reasons: A) because she is insecure and NEEDS to show you off to her FB friends and family. Or B) because she is proud and WANTS to show you off to her FB friends and family.
Either way, it is worth confronting her and asking her first, before jumping to any conclusions. Just ask her the same way you asked us here, but do it calmly and try not to judge before she speaks her story. Good luck.

You still seem pretty confused about whether a very possessive and insecure person who does not respect conventional boundaries is a good or bad thing. It shouldn't be hard to pick the right answer.