To to be honest, I think you were over-reacted. It is true that no body likes negative feedback. But keeping a positive attitude is very important. What you should have done is to thank her for the feedback first. It's ok to give her your perspective, but in a more constructive way. Instead of saying I don't agree with your rating and I won't sign the review, you could have said I would like to read the review more carefully and get back to you on the signature after I understand the HR policy about 2 rating.
Now about your communication issue. It's not uncommon to see first generation immigrants having communication challenges, especially verbally. Even though your boss seems micro managing, you can still learn from her coaching. Again, keep a mature and positive attitude. Get a mentor, actively seek for real time feedback after meetings, etc. There's always room for improvement even though you don't think you have any communication issue. Keep your boss posted of your progress.
Bottom line, those things happen. Sometimes it's better to move on. Admit our issues and improve. If treated unfairly, move on. Change department or company. But un-admitted weaknesses will follow us anywhere. You need to be honest to yourself.
Very few people can have years career with no down period. Actually...practically nobody. I know I have mine. So cheer up and keep your chin up and enjoy your weekend! Tuesday will be another day!
