once baby's head is engaged can it come back out? Or be moved?
It can, but it generally doesn't. If baby is malpositioned, sometimes a midwife will have you in an inverse position to try and disengage baby's head to turn him/her into a better position.
her head is deeply engaged chked by u/s, internal exam and external exam but she is facing to the left...I think this is what is holding things up and causing a lot of the pain. I'm going nuts rocking and being on all 4's but every day the u/s is saying the same thing. my daughter was face up like this and stuck