Under Admin, under Pages, I deleted a page and all of its sub-pages and their sub-pages went away also. Why would this happen? Can I get them back or are they really gone?

It might, depending on what version of DNN you have. I posted a bug report to Gemini a few months ago that pages deleted in the Admin | Pages area bypassed the recycle bin. Not sure what version got it fixed, or even if it is, actually, as I haven't checked.

What is supposed to happen is that when you delete a page, it gets put into the Recycle Bin. So go to Admin | Recycle Bin and see if you can find the page you deleted. if you can, you are in luck ... restore that page, and then go to all its first-level children, one by one, and move them to a different parent page. Then you can once again delete the page that  you don't want.

Good luck ... !

Thank You all for your replies. You were correct and problem solved. You just saved me about a weeks worth of work.