what do i do now?

I am 25M doing my masters in XYZ College in India and there is one of this girl 25F doing her masters in same college but different dept, though we know each other from very young age we don't actually talk, we even attended same tuition we never had a talk.

Growing up she had her marriage and within a year she got divorced and fell into a trauma and now she started to recover and doing very well , she have no guys in her Instagram id and she never accepts even guys from our college, I started to develop feelings for her lately and then i couldn't stop thinking about her, she quite often shows up in my dreams, making me realize i started falling for her.

But the thing is idk where to start since our families are already having a cold war and clash happening , her friend also tried me so bad and i wasn't giving much attention to her because she started to behave weirdly, being the popular main character of my department i am pretty much sure she would have heard all the negative comments and rumors and about my past and present that her friends and other students made about me in the campus, there is also this other rumor in college that we both are seeing each other in college and one of my friend told that she doesn't know about that rumor. Sometimes we used to talk about the professional college stuffs only in person that too for very few mins and then we leave, when it comes to social media i used to text her asking the professional stuffs and she replies to the maximum and no extra chats , not even 0.1% extra and i think she also knew that i am showing some interest towards her and i am not sure about that too. I don't know what she is thinking about me only.

So guys kindly share your opinion and give me some ideas to grab her attention and at least that i could have a general conversation other than professional stuffs in person or in chats.

somewhere my instincts says that she likes me too like 30% not sure but what if some bad rumors about me and comments on my past made her feel not to talk with me or see me further since she have already gone through something big in her past.

I am developing all sorts of questions and asking me and getting too much confused all these days, Kindly share your comments on this.

Thanks in advance :)