From the flashbacks we've seen of her past, she was kidnapped and tortured to death so why was she in a mental hospital?
Exactly that...She was kidnapped and tortured. That kind of trauma can have a host negative effects on the mind. Extreme trauma is known to cause depression, bipolar syndrome, schizophrenia, and a number of other mental illnesses. Chances are that she had one or more of these severely enough that she couldn't function in a normal setting.
She wasn't killed. She was kidnapped and tortured which left her "damaged" like the episodes title.
This, exactly. Also, she had Slayer visions that further compromised her grip on reality.
I thought she was hospitalized because of her visions/dreams of past Slayers' lives.