can a 13 year old move out?

only if the CPS move you

You can live with your sister and she can become your legal guardian. The court system is very good at giving legal rights to a family member if you wish to get out of your situation. If you don't get your sister to do this you will probably go into foster care if you turn in your mum or run away.

That would be between your mother and your sister. If you mom wants to keep you then you should just try and get along. It's a very sad situation. Focus on your school, and work towards a career one day.

You have to live with a legal guardian until you are 18. If your sister is 18, I thinks she can adopt you.

Yes. You will need to go to court and get emancipated for it to be done legally. You have a good case considering what you have at least told us your mother does. Courts are very partial to children when it comes to irresponsible parents. (So they should be!)

Yes, your sister can become your legal guardian which means she is responsible for you instead of your mother.

If you are smart enough to know you are in a bad environment, then you are smart enough to know that your sister's is a better place to live.

Good Luck!

CPS can help you. Your mother can get in loads of trouble, legally, for neglecting you.

With the government's permission, yes. Not on your own, obviously.

If your sister and mom agree, yes. You can't just run away, tho.