John, she is going to die. Had my parents known that I was taking everything in and making my own sense of the strange words they were using, I am certain that their vocabulary would have been much different. If your conversations are private, take them far away from your children.
Children hear everything.
Don't assume they are sleeping when their eyes are closed. Explain the terminology. Surgery, operation, testing etc. There's nothing worse than feeling scared and confused and not being able to talk about it. Here are some things that used to made me feel so guilty for being sick and needing to go the doctor.