Your question really doesn't make sense. Obvioulsy English isn't your first language.
You can buy a home. Anyone can own property in America. You might not be able to qualify for a loan and that is different than being able to buy. Loans are given by banks based on the person's past credit record. If you have no credit history you can't start with a mortgage.
I have no idea what the children and University have to do with the situation. Contact an attorney that specializes in immigration and can speak your language for further advice.

i am waiting for the answer about my question.