It's normal, but some of it's not acceptable. Yes, they pull away and get info themselves, and there's some shoulder shrugging and eye rolling. There may be a lot of "I don't know." They are figuring things out in some cases, and of course they're starting to become more independent which means parents aren't cool.
Lying about who her friends/contacts are? Nope nope nope. I'm not sure how you figured out that the "girl" was really a boy when she lied about it. Were there photos?
Anyway, her phone is not hers. It's yours. She has no expectation of privacy while she is a minor, short of you not going into the bathroom when she's there and short of not going into her room until she's dressed. If she cannot handle a phone responsibly, she loses it.
I don't think you have to grill her about every little thing - the independence is normal, as I said, and she needs to "practice" being an adult or at least an adult-in-training. But kids who don't respect their parents and who lie are going down the wrong path. That means you don't interrogate her or expect to be her best friend and confidante (if that's what you mean by "reconnect" with her), but you know what's on her phone (contacts, apps, photos, videos) and you police her social media accounts. And if she walks away from you when you're talking, she's too immature to have a phone or a computer. You need to get a handle on this and set some ground rules before she's thinking about a learner's permit or going out alone with friends. A kid you can't trust is going to be a problem - and she needs to know that now. If she wants privileges that go along with being older, then she needs to demonstrate that she's mature enough to talk to you. Kids who have parents who just look the other way can wind up dealing with drugs or naked photos or booze or vaping.
You can also try talking in the car - no eye contact works well for a lot of tweens and teens. And they can't walk away but the talks can be limited in scope due to short trips here and there.