The lighter colored and darker colored bills (as well as down) is how you identify the gender. The darker are the female, the lighter are the male. You can tell the difference between solid and saddleback with both male and female, but it's a lot easier on the females since they have darker coloring. The solids generally don't have splotches of dark, the saddlebacks do. The easiest way to tell a saddleback is if it has grey on its head then a yellow neck and grey again. It takes some practice and I even mix them up a bit after doing it for years.
I have had mommas squash their babies. I think it's a new mom thing as my older girls have never done that since I've had them (they were older when I bought them)
Aurorasprings, why don't you post some pics and we'll try to identify them?
I agree that the squishing is an unexperienced/new mama thing. Thats why I am pulling any goslings my girls hatch this year until the babies are a bit more hardy. The geese I have sitting are probably just now about 1 year old, so they have a strong mothering/setting instinct, but they still have learning to do on how to take care on newborns, and I just don't want to risk it.