同情你too. but

I am not a lawyer, but I would give your some comments hope you don't mind.

1. It seems that you need to improve your language a little bit. Don't any written document by you unless a native speaker proof-read it for you.

2. Don't acuse your Africa neighbor if you don't have hard evidence.
3. Document everything, including: copversation with you neighber, social worker, etc. Be calm all the time.
4. Copy all the documents you have received. Certainly if the statement contains false information, it is good for you. If you can prove that your Africa Ameican neighbor is lieing, that you have a good chance.
5. Be calm all time in court,try to get sympathy from the judge but don't dry hard.
6. Defend yourself, be brave, be strong.

I have to point out that you should not let your neighber get control of what you need to do or not to do. You should just ignore whatever she wants you to do such as buy an air conditioner, what the hell does it to do with her? If she think you make outrageous noise upstairs, she can simply call the police. You have every right to refuse her entrance into your property(apartment), even with violent means should you choose so. You are the mother, you are the guardian of you son, how could you let someone you don't like stay with your son without your presence?