RE: egg hatching??
My father and I raised pheasants years ago. We've had pheasants escape but they would still hang around the house. We would see them from time to time. They must do OK with raising young because a few times we would see chicks with them. Unfortunately the fox, hawks and owls must have gotten them because by the end of summer we didn't see any pheasants.
On another ocassion, I had hens set on eggs and hatch them in the pen.
Be careful with the roosters in the spring. They will fight all the time and kill each other. We use to section off the pen and put one rooster in with about 6 hens. Sometimes we would trade roosters with other people that raise pheasants. We did this to get a different blood line and prevent inbreeding.
Try to catch that hen that escaped at night. Put some feed out scattered around the outside the pen, to keep her around. In the evening, if you see her, keep an eye on her until after dark. Then get a large fish net a catch her.