Out of curiosity, I asked my DD (3.5) to explain what a star is. She was on an astronomy phase forever and still comes back to it once in awhile so I know she knows the correct astronomy definition and she knows that I know that she knows.
Me: "Can you tell me what a star is?"
DD: "Me!"
Me: "Yes, you'll always be one in my eyes but pay attention to the question because you didn't answer it. Can you tell me WHAT a star is, not who."
DD: "Nope" (twirls around and escapes to another room)
This is exactly why I am worried that if we decide to try her out to fancy private schools, she won't be accepted.
Nautigal, if your DD has gotten better over the years, it could be largely developmental but you mentioned that she seems stuck when it comes to taking tests. Maybe an evaluation won't be a bad idea.
A series my SLP friend recommends for young children who need help with answering comprehension questions is Franklin because the problem and its solution are always very clearly defined but your DD is most likely too sophisticated for that. I'll try to think of a more appropriate series for older children.