Atheism is a complicating factor in your life, because you would get along more easily with your mother if you shared her religious delusions, but the basic problem of how to survive in our world is more financial than religious. All the questions that you ask, for a financial plan, suggestion about where to live, how to save money, or whether ask friends if you could stay with them, are not religious issues. Lots of people have economic problems even though they have no religious disagreements with their parents. You also have serious psychological problems indicated by self-harm, stabbing yourself with a pencil. You should always be your own friend no matter how hostile anyone else may be. But I realize that when you do not know what to do, you feel the pressure to do something, even if it doesn't actually help you. But please don't harm yourself. Despite all the problems, which are very serious, you are still a young man with the potential to have a long and productive life.

Bear in mind that there exist government agencies designed to help people who are in trouble, and you might need to consult one. Other than that, yes, staying with a friend might be an excellent move, although I do not know you or your friends well enough to really know. However, it often does help to pool your resources, when struggling for survival. You should not have to live in the streets (as you envision) even if you have the lowest paid job - incidentally, the minimum wage was just increased in California to $15/hr, so even the lowest paid job will pay reasonably well per hour, although you might get only a part-time job and therefore still have a low income. If you have a shortage of money even when you are working (which does happen to some people) you can economize on housing by sharing your housing with friends - as long as your friends are honest people. Such arrangements have the potential to become more trouble than they are worth. But they can also work successfully.

While I cannot know what is going to work best for you in terms of specific jobs, housing, education, psychological help etc., I can give you some general advice which is not to give up too easily, and to keep trying things. If something doesn't work, try something else. When I was your age I believed that my life was hopeless, that nobody would ever hire me for any job, or rent me any housing, or help me in any way. My father was at the point of killing me (and he specifically told me that if he did kill me, he wouldn't care). But I took risks and some of them worked out. It turned out that I actually was employable. I had a skill, which was that I knew how to type. Not a hugely impressive skill, and yet, it did make me employable. You probably do have some abilities which would make you useful to at least some employer somewhere.

Even the fact that you do have friends (which must be the case since you mention that you are not sure if you should ask them if you can stay over) means that you do have something to offer. You are likeable enough (for whatever reason) that there are at least some people who like you. And I believe that there are other people who would like you if they met you. I would probably like you if I met you, but that is not going to be practical due to our different locations (I am not even in the US). That is pretty much all I can tell you.