Does iOS backup include the OS and related questions
No, the backup does not include the operating system. However iOS can be easily downloaded from the internet, so that is not a limiting factor in itself.

The main problem is that you cannot downgrade an iPad to iOS 8 at all. The original iPad only supports up to iOS 5, and the next-oldest iPad - the iPad 2 - supports iOS 9. As it is only possible to downgrade to the iOS versions that Apple actively is signing, which only includes the latest versions available for the hardware, you're out of luck.

Your only possibility is to buy a used iPad that has iOS 8 on it.

I would recommend instead getting an iPad with a newer iOS, as there's serious security implications to running older iOS versions - and then search for a replacement app, or ask the original developers if you can convince them to update the app for newer iOS versions.