How to make an independent woman like you? How to know if she like you? How to show her you like her?

I met this girl a few weeks ago and she is a very amazing and independent woman (it actually took me four months of courage to approach her). I don't know if she knows I like her but whenever I see her at the dining hall I would go and sit down and talk to her. When we are eating she would usually be on her phone but would look up and smile a little at me when we talk. I'm usually the one that talks more and asks the questions and recently I'm beginning to feel like I'm annoying her. I followed her on Instagram but she didn't follow me back. How do I tell if she doesn't like me or if she finds my annoying and if so should I continue talking to her. Can she tell that I like her and how do I show that I like her? Is there something that I can do to make her more comfortable talking to me?
How to make an independent woman like you? How to know if she like you? How to show her you like her?
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