It sounds like this student has a problem with expressive language; he is receiving and processing information correctly, he has trouble communicating what he knows.
Standardized testing is one form of assessment used in schools. Find out about standardized tests, how and why schools use them, and how you can support your child.
From your comments, I am concerned that this private, independent school is not equipped to provide the necessary special education tutoring and accommodations.
You note several possible reasons why your daughter might not have successful social interaction skills. Her ADD, OCD, and lack of confidence might be the issues. Start with the school counselor.
You mentioned that your daughter retains information from TV shows and comic books, so you may want to consider using multimedia to help your daughter learn new material.