Do iPad apps work on iPad PRO and vice-versa?
That depends on how the app was made.

Apps are meant to define the position of interface components in terms of their distance from the edges of the screen by using a technology called AutoLayout (included in Xcode, the development environment for Apple devices).

If the app was made with AutoLayout then yes, it will scale.

As for whether or not they will work, iPhone and iPod apps can already be used on iPad so there should be no reason for which iPad apps shouldn't work on the Pro.

However, when the interface contains a lot of stuff and the interface was designed for a bigger screen, the components could get squashed together. If particular technologies are required (e.g. Apple Pencil) they won't work on the regular iPads.