Wrt non custodial parent: you will need your school principal and/or a clergy member or doctor to certify that you’ve had no contact with your biological father for years, that he’s had no presence in your life, and that no one knows where he is; further, that no one in the family or among relatives has tried to find him due to his issuing threats which the mother didn’t know we’re illegal, so that right now the school wouldn’t provide information about you if he were to suddenly manifest himself and ask for it as he has severed all rights over you. <= Or whatever applies!! This is a maximum case.
Most colleges with a custodial parent waiver form will accept this type of official statement with the form. Some don’t so you better find out right now which ones have the waivers and what sort of documentation you need.
The best solution indeed is for you to try and get the highest possible scores on the SAT (will your school cover the costs?) Then, apply widely. Considering your mother’s income, you’ll get an application fee waiver on common app. It’s going to be a lot of work.
Plan to move to the US as soon as you’ve graduated. Missouri and Utah would consider you instate after a year of work there. They’re the only two stated where you can work, attend college w and after a year be considered a resident.
You can also see if your relatives can take you in and from there you can commute to work.
If you belong to a church or mosque, does it have connections in the US?
That way, if you aren’t admitted to a meet 100% need school through Questbridge or on your own and can’t get sufficient merit aid somewhere, you have solutions that allow to live in the us.
As for sponsoring your mother and sister, you should definitely try to do it if you have a job, as they’d be safe and your sister could attend ba public school, but I’veheard that for parents it takes a long time, like many years, so you would have to start as soon as you think you can.
Can’t your mother stay in Kenya? Turkey is dangerous right now - lots and lots of arbitrary arrests. So many teachers were arrested that back to school had to be delayed by six weeks. Contrary to the Kemal legacy, “revisionist” islamist thinkers are taking over the school system and targeting girls education. It’s not safe for your mom or your sister.
(Granted, Kenya is very unstable too 
)
So, recap
- meet need colleges (especially in the Midwest since they have fewer applicants. Colleges such as Carleton, Macalester, Grinnell, St Olaf, but also Lawrence, Gustavus Adolphus, Beloit…) + Questbridge
- merit scholarships - pay attention to the deadlines. AES at UTD, different scholars programs at IU or App State, Montana State, etc.
- relatives that could host you
- Missouri (or Utah) to establish residency