I have a few thoughts.

First, I think there is nothing wrong with not wanting kids. Not everyone is cut for it. I actually think it's great that you know that about yourself and have chosen not to have them.

Since you say you don't know a lot about kids, I want to reinforce that the 11-year-old girl's behavior sounds totally and completely normal. She has been living apart from her father and with a mentally ill mother, so the girl's emotional needs are not being met. Most likely, no one has been paying adequate attention to this little girl. I would NOT call her behavior attention-seeking. I would call it absolutely normal and probably necessary in order to make sure her basic survival needs are being met. She has clearly been through a lot and she has been missing out on the experience of having a dad in her daily life. She really deserves a lot more attention than she has been getting. I would definitely not shame her for this or criticize this behavior or label it as MI. She is behaving like 11-year-olds behave under normal circumstances, let alone kids like this who have been missing out on parental attention.

Even if the little girl WERE behaving inappropriately, it would not be her fault or her job to change herself. It would be a reaction to her surroundings and poor parenting, and it would be up to your boyfriend to gently encourage different behavior without ever shaming her or identifying her as "the problem."

Your boyfriend's attention really needs to be on his kids, especially now, but really all the time. His kids Will always be his #1 priority. Since you say you have BPD and need more attention than the average person, this might be a problem for you in the long run. Not everyone is cut out for being #2 (or #3 or #4). If you know that never being his first priority is a problem for you, then I would re-evaluate things. If you don't want to be a step-mom to his two kids, I would re-evaluate things. If you don't want to be part of this family, I would re-evaluate things.

Even if you were someone who loved and desired kids and treated this little girl with the utmost care and love, she still might not want you in her dad's life for no other reason than you are not her mom. If that happens, your boyfriend will choose her over you. (I say this because I have been there, quite recently. I was in a relationship where the 13-year-old daughter wanted her "old family" back. She liked me as "the friend" but threw a tantrum upon being told I was "the girlfriend." She ended up throwing tantrums every time my partner was supposed to see me until my partner chose to end our relationship in order to take care of the daughter's feelings. I absolutely want kids & tried everything under the sun to win over the daughter, but there was nothing I could do. She wants her "old family" and that's not me.) I say this just to demonstrate that the kid wil always come first, and if the kid doesn't want you there, your relationship might end regardless.

Being the "girlfriend" in someone else's family always means being an outsider. If you've already felt like an outsider for much of your life, it's really hard to accept being an outsider, forever, in your "chosen" family. You will never be the kids' mom and they WILL at some point yell things at you like "you're not my mom! You can't tell me what to do! I wish my mom/dad never married you!" It HURTS. It sucks. Even when the kids love you, they are still kids and they will say stuff like that in moments of anger. It's a really hard position to be in. It's not for everyone.

I would really think long and hard about whether you are prepared to handle this situation. I say this because I've been "the girlfriend" more than once. Both times, the relationship ended not because of the relationship between me and my partner, but because of the kids/blended family situation. Once, because the daughter wanted her old family back and once because I wanted to have a baby and my partner didn't think having another baby was in their kids' best interests. Because the kids will always come first, you are the one who is expendable. You have to be ready for that going in. Honestly, I don't think I would do it again. I still want my own kids, but I don't think I will date someone who already has kids again. I'm okay with my needs being #2, but I'm not okay with the idea that my relationship could end at any moment if my partner's kids don't want a step-mom and my partner honors that request. (Of course, no kid should have a "bad" stop-mom, but I genuinely cared for the kids and we got along beautifully up until they realized I was becoming "permanent" and that meant their parents were not going to get back together).