I am trying to find out about my Armenian heritage

I’m sorry this is going to be a long post but I recently found out the my (f21) dads side of the family is Armenian and I am trying to learn more about my heritage. I don’t know a lot because I only have a few documents and my grandmother died when I was young and I didn’t have a lot of contact with her as we lived in different sides of the US. But I’m hoping for a little help in connecting the dots, because none of the dates on the paperwork we have line up like at all.
So what I know so far is that my great grandma escaped during the Armenian genocide and made it to Rhode Island. While she was in Armenian she was married 4 or 5 times and had we think 2 kids. As she fled we have a record of her leaving one kid in Syria and another in Lebanon and then heading to the US from France. The next paper I have was her petition for naturalization which said that she got to RI on November 6, 1913, but the petition wasn’t filed until January 20, 1922. So somewhere between when she left Armenian and got to the US she had my grandmother. We don’t have a birth certificate for my grandma Mary but we do have an Affidavit of Birth, which says she was born in Rhode Island in 1918. But from what my parent have told me, Mary said that she thinks her mom lied about dates to qualify for naturalization and the get her US citizenship, or there could have been difficulties with the language barrier, so I am not sure how much of what I have is accurate.
On the Petition for naturalization my ggm listed 5 children with Mary being the youngest. We know one was in the US with Mary (Micheal) but have no idea where the other 3 ended up or if Mary had any contact with any of her extended family. But from what my mom remembers from talking to Mary, she said that her mom was born in disputed territory so on her birth certificate is says she was born in turkey, but she always said she was Armenian, and we know all of her husbands were Armenian.
Any direction for finding records in Armenian around that time or help deciphering what I papers I have would be appreciated, I will add photos. My family is not super knowledgeable just because Mary was my dads mother and he is 15 years younger than his next sibling so they are not close and do not talk and my dad never really cared or asked his mom anything about their heritage. The only reason I know anything that Mary had said was because my mom is like obsessed about genealogy and talked with my grandma before she died. Thank y’all for reading and hopefully I can find out more!