A soft shell is not a good sign. Do you have a UV lamp over their tank? If not, they need a UV lamp! You might want to put extra calcium in their food by putting calcuim powder on it.

I would definitely get a lid for the tank! I don't think Nero pushed Mashi out, I think Mashi climbed out on her own.

Without seeing pictures it is very hard to tell if they are boys or girls. In some species of water turtles, the boys have VERY long front claws. If either of them have very long front claws, they're probably a boy.