Is she really crazy?

I think it's a reasonable question, because going insane for the rest of your life and talking nonsense and roaming around dirty and uncombed isn't quite the reaction most of us would have to Song Lian's experiences. I know it was rough, but still.

There would be a LOT more mad people in the world if it were.

~~~~~~~
Have another bite of popcorn and forget about it.

I see the movie as basically a tragedy, and so, yes, she is insane at the end.

I think "insane" is a vague word, and it's best to not get caught up in it. The important point is to try to understand her mindset at story's end. It's a powerful, haunting, disturbing image: Like her experiences blew a big, gaping hole right in the middle of her neural net.

I think that's the important idea. If you don't cry at the sight of her state of mind at the end of the movie, you missed the point.

Yes, she did go insane.

She caused the death of the one person she truly cared for in the household and the only person who understood her. She couldn't take living with the guilt nor ignore the fact that she was married to a Bluebeard murderer.