Well, analyzing the scene: Baby Doll escapes from the window at the same time he opens up the “closet” where her sister is hidden. Maybe, because her stepfather locks her at the same time her sister runs away, so everything happens in parallel. She’s outside the mansion. It’s supposed to be a mansion, I guess. So, until she enter the mansion, search for a gun and go there, would be enough time to her stepfather kill the sister, somehow. When she shots, it hits a lamp and a gas tube. Her sister would be down, in the floor. How could the bullet go up and down? Unless it was “folded” by something, it is impossible. Here is a print screen, where you can see the lamp and the tube:

I’ll leave you guys make your personal judgement. It’s great to pull that kind of subject off, though.
At least you know what is Google? Because I’m starting to think that you’re joking with me, I’m sorry.
Yes, it looked like she shot her, cause when she came up, her sister was bleeding. My fault.
No, she killed her sister. At first, he was going to kill both, but Baby Doll picked a gun. In self defense, she was going to shoot the stepfather but she missed and killed her sister. This whole scene is right here.
Ok, look, there are 3 layers. 3 layers inside the whole movie. First layer: the reality. She was taken to Lennox House because she killed her sister. 5 days later, the doctor comes to make the lobotomy. In these 5 days, she planned her escape with her friends, but wouldn’t be the movie so exciting if it was told normally, would it? Then comes the second layer. The brothel. All the characters are the same, in different ways in the brothel. Her dance and what happens while she dances are part of the third layer. Is a really deep place into her mind that she reaches while she dances. The last 2 layers are into her mind only. The second is the mirror of the first. Don’t compare both movies, they are pretty much different. I used “layers” because Zack Snyder used the same thought in this interview. (the article and the subtitles are in Portuguese) In Sucker Punch, we see the reality, the “mirror dream” and the unreal. That’s it.
Her dreams comes in her mind as flashes while the doctor does the lobotomy. But her dreams are the true, which means she really tried to escape Lennox House. Remember “Reality is a prison; Your mind can set you free”? Still, the brothel isn’t real, Lennox House is.
Yes, basically, that’s it.
Probably the mental hospital. I have this personal theory that the brothel where they are is the reality, but as a dream inside Baby Doll’s head. You see, Madam Gorski was the therapist, but in the dream, she was the dance teacher. Blue was the supervisor of Lennox House, while in the dream, he was the supervisor of the brothel. The only thing is the end, like “what happened to Baby Doll?”, but if you could see the removed scene (at the Blu-Ray version), she was with High Roller, in the brothel, which means she surrendered to him. (you can see that in the mental house, when the doctor makes the lobotomy, is a alternative reality, so what happens in mental house, happens in brothel and vice versa)
At first, I thought that was something different that everything Snyder has ever done. He’s an amazing director and his jobs become differently in every movie. When I first saw Sucker Punch, wasn’t so hard to understand the storyline and that everything, besides it’s a dream, it’s actually the reality told differently. The personalities of the girls represent something special for me, tho. They have so much in differences and they become friends easily. The end is not like “omg, so unexpected”, but is a life-lesson too, that sometimes, we’re not the protagonists of the story. It isn’t my favorite movie, however, I love so much watching it and everytime I do, I love it more. :-)

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