It sounds like both of her biological parents are doing a lousy job of it and your dsd sees you as the best parent she has.
She has been texting me all day, sent me pics. So I will keep that as a proof. She is much more talkative now. Her main worry is that her sisters are going to be separated. Also, she doesn't feel comfortable with sharing room with boys ( I didn't know that beforehand, I assumed she was with her sisters)
and previously:
I then asked if someone was hurting her in the house , to which she said yes.
This really is completely unacceptable for a 14 yo girl to be sharing a bedroom with two older step brothers. And they're technically adults at 18 and 21.
Something is badly wrong here, and you'd be irresponsible to not alert the authorities. You really, really need to be contacting social services about all these issues (and there are loads from what you're saying). The school meeting obviously went badly because dsd's biological mother was there and dsd has already said she's concerned about getting her mother into trouble. So there's no way she's going to speak openly with her mother about. Social services know how to handle these situations, and they always make sure to speak to the child without the parents being present.
DD (kinda) gave me a hint that she would be at her dad's for summer holiday. So I am wondering if I should go back with him so I can spend the summer with her.
Be cautious about this - it could just be a ruse to lure you back in. Either her dad using her as bait to get you back or dsd trying to manipulate you (can't blame her for trying) into going back so she can spend time with you. If you go back the status quo will continue.
Unfortunately, I doubt I can do anything for Anna. I guess I we will text until she is 16 - THANK YOU FOR THE PERSON WHO TOLD ME 16 IS THE AGE YOU CAN LEAVE- and she will have a home to go to.
She asked me to adopt her, live with me, change her family name to mines. I explained to her that it is not feasible. She is upset, but I have no official relation with her.
Unfortunately, she is currently probably feeling abandoned and let down by you as well. She sees you as a parent, and she won't understand the legalities over the emotions. However, if you let dsd come and stay with you I think it would be be a good step in the right direction. As long as she's there of her own free will, I doubt the authorities will remove her from your care (certainly not until they've established WTF is going on with her home life. And she's right, they won't let her live with her mother in the current circumstances, and they might consider taking the other younger kids into care as well.
Obviously doing this will burn bridges with your ex partner, and ultimately ss might say that dsd should go and live with her dad. Assuming he'd agree to have her full time, because it sounds like he doesn't give a shit, and is even less likely to want to without you being there to do all the work. Actually, he might decide he wants his daughter - but as a domestic slave to replace you, which would be almost as tragic as the current situation.
At 13, my friend's ds packed his bag and ran off to move in with his 16 yo girlfriend (in her mother's house). Police were called and went round there, but said he wasn't in danger and wouldn't remove him against his will. Despite them admitting that they were sexually active and the girl's mother wasn't even trying to deter it from happening under her roof. Thankfully his parent's talked him back home after a few days.
I think if ss saw the full picture they would be reluctant to remove her from your care, and even if they do, it might take months to resolve and reasonable chance they'd let her stay with you while they investigate. In your situation, I'd probably take that chance.