Hi there,
First of all, if there is some kind of friction between you and your mother, I suggest you speak to a school counselor or teacher you trust to see that you can finish high school without any issues. Secondly, if your mom is kicking you out there must be a reason why. You know yourself if you are giving her reason to do so by your behavior, or maybe she is suffering with her own issues and is stressed. I don't know. But please do get some kind of counselling whether it be with school or one of the hotlines out there. Or even a church group. As for a job, it is more difficult to find a job without a permanent address. Employers want to know you are reliable and will be there every day. If you are homeless or have no transportation, home, you may not be able to be contacted, etc. and that is not good for them. Are you going to college? Why not look into college and see if you can live in a dorm. There are lots of scholarships and financial aid for good students who have no money. Maybe you could live on campus and get a job near the school.
Anyway, you sound like an intelligent young person. Right now the economy is bad so the fact no employers have called, may be just due to the economy. If you want to land a job, you need to know just how to fill out the application, answer questions correctly, and then call them with a follow-up call asking about the job. If it is filled, ask why you weren't considered. Take their comments in a constructive manner. It will help you for the next application. Try getting a job at McDonalds or a supermarket. Those places always hire.
Good luck and let us know how you make out.