Hospitals, nursing homes, any type of facility that sees a significant number of deaths have a reputation for being haunted. We've had several people in the health care profession here on this board who have reported paranormal experiences in their places of work.
The sound of the baby crying and the nurse in old fashioned uniform could be what is called a residual haunting. The best way to explain that particular phenomenon is to compare it to a tape that has recorded an image. In those types of hauntings, it is like the area has absorbed some small bit of time and plays it back periodically. Those type of spirits typically do not interact with the living -- we see and hear them, but they can't see us.
As far the incident in which the elderly gentleman passed away and your co-worker experienced something upon entering his room, she could possibly be what is called a psychic sensitive. Psychic sensitives often take on the physical pain they feel another person is in and it effects different people in different ways. I would be curious to know if she had ever had a similar episode. If she has, she might want to consider a profession other than something in the medical field!
It could be that if the gentleman had been in physical discomfort at the time of his passing, your co-worker absorbed some of that feeling and it manifested in physical discomfort for her. If you've ever been in a room where people were arguing just before you entered, it is similar to that. You walk in and you are just dandy, then you sense that something is not right and your good mood is toned down a bit. Other folks may have some more theories.
I think you are doing the right thing by seeking answers to things you have experienced. The more you know about something, the less likely you are to be frightened of it. Good luck and keep your eyes and ears open! Let us know if you have any more experiences!