If I am emancipated, and still attending school but I'm staying with a relative, would I be able to apply for some sort of cash assistance and or medical insurance/food stamps?

In order to become an emancipated minor, you must petition the court and meet certain criteria. See our information on Emancipation to learn more. Each of the programs that you mention in your question have their own set of requirements in order to be eligible for the program. Check out the Arizona Department of Economic Security website to learn more about the requirements for each program.