Grandma is naturalized ~ the problem of my getting a green card

Mom's age is there, and divorce will not affect the approval, and it depends on relatives, not getting married in the past, nor for the purpose of marriage. The queuing time depends on the backlog of cases, which will change from time to time. If you are underage, you should apply together with your mother. You must apply separately as an adult, an independent case.

Since I want to study abroad, I'd better study abroad first, and then apply for immigration with my mother. Applying together will complicate the situation and may take longer.