Translation:Her head is injured.
I'm pretty sure that "She hurt her head" is also correct. 了 indicating the past/change and all.
Yes, that's should be correct.
Not to be pedantic here, just FYI, the literal (and not passive) translation of your sentence could be “她 伤/弄伤/搞伤 了 (她的) 头/头部”. 头部 = head + part.