I am a mother and my heart is breaking for you. I have a teenage son (well, he's 18 now), so I understand the need for kids to have their own space and to have privacy. What your mother is doing is horrible and let me just say that it is NOT normal. What your mother is doing with your social security card is illegal - it is considered fraud and she could actually go to prison for doing that. The food stamps are NOT hers. She is only able to receive food stamps because she has children. Unless she has a disability or is receiving welfare because the government is requiring her to look for work while receiving benefits, the only reason she is even able to qualify for food stamps is because of her income level and the amount of children who are her dependents. I know this from personal experience because when I was married to my ex-husband, we were on welfare and food stamps for a time. If your mother is able-bodied and capable of working, she cannot just get food stamps for herself only. No matter what, because she is providing for you and your siblings, then the law will say that the food stamps are for the family, because the amount your mother receives in food stamps is based upon a family of 4 or 6 or however many people live in your home.
Let me just say one thing about your mother telling you that she regrets having you. Any mother who would say such a thing to her child is horribly cruel. As a mother, I can tell you that unless your mother is a horribly dark-hearted woman, she does NOT regret having you. No mother, unless she is completely heartless, regrets having her child. From the moment a woman first feels her baby moving inside of her, she begins to develop a love or connection to that child. When a mother holds a baby and is amazed by the sheer miracle of life that she helped create, a bond is created. Now your mother might be very unhappy with her life and the friction in the home and with you might be such that she gets very upset and frustrated with you. When parents are frustrated with their kids, they will often say strongly worded things to get their message across that they are upset. Still, that doesn't mean that they mean everything they say. I think that from what you have described in your question, that your mother is just a very unhappy and stressed woman and she is taking it out on you and your family. That is sad. Please don't believe everything she says about you as being true. She is hurting and feels better when she can make you hurt as well because then she doesn't have to hurt alone.
Now for what you can do about this? Well, it sounds to me like you need to live elsewhere. Your parents should not be pressuring their children under 18 to get a job so that they can charge them rent to live in the home that it is the parents' job to provide for them, when the parents themselves are collecting welfare and food stamps. The parents should be working 2 or 3 jobs if necessary to provide for their family. If they have to supplement their income with welfare, then so be it. Sometimes it's hard to find adequate work and people need welfare to help them out. That's what it's there for. It sounds though like your parents are abusing the welfare system and trying to take advantage of welfare and their own children. You sound like you are in a very unhealthy home.
You also sound like considering the homelife you have, you have a good head on your shoulders and are pretty mature for your age. You can legally declare emancipation from your parents, which would mean that your mother cannot legally claim you as a dependent and she would lose the amount of welfare and food stamps she was getting based upon you being a dependent (however much your portion would be). You would then be able to move out if you wanted to and have the legal rights of an adult, I believe (not voting or buying cigarettes, but of obtaining your own apartment etc).
My suggestion would be to contact your department of social services in your area. Call them on the phone or go there in person if you can (be prepared to be there a long time if you go in person). Tell them your situation (social security number usage, your mother claiming the food stamps are hers only, parents putting pressure on you to get a job so they can charge you rent etc). You could simply call the Child Protective Services Number in your area and make a report. These reports are confidential and your parents would never know that you reported them. Anyone can make a report - a neighbor, relative, friend, doctor, social worker - anyone who suspects anything that isn't right. Therefore, there is no way that your parents would know you made the report if you don't say anything to them or your siblings about it.
Social Services or Child Protective Services can launch an investigation. They may try to remove you and your siblings from the home and put you in a foster home. This is something that you should discuss with the person you are talking to, if it is a concern for you. I know there are horror stories about foster homes, but there are also so many wonderful, loving foster families that help provide safe and secure homes for people in your situation. A social worker can help you figure out the best way to get help in this situation. You could also talk to a Youth Center or a pastor or priest at a local church. They can advise you. If you have done nothing before school starts, then when you go back to school, you can talk to the principal or a school counselor. Schools are mandatory reporters, so anything you tell them which will raise concern, they are obligated to report. You can get help that way. Whatever you do, talk to an adult who can help you. As a mother, I am concerned for you and your siblings. You should get out of your home as soon as you can. Your mother is not only breaking the law, but she sounds as if she is mentally unhealthy. You will only be in for a miserable couple of years until such time as you become an adult and can move out on your own. You shouldn't have to live like that. Best of luck to you. I will be praying for you that this situation will work out for the best and you will get whatever help you can.