Can a .dmg file be converted to work on ipad?

Actually, the file format itself isn’t really the issue. If you have a dmg file, that would be code compiled for OS X and simply cannot run in iOS at all. And there is no way to install it since the sole supported installation portal for iOS software is Apple’s App Store. You cannot download things from web sites and install them to iOS.

App code needs to be compiled separately for each specific operating system - be it Windows, OS X, iOS, Android, etc. Code compiled for one is not compatible with the others.

No they are two completely separate operating systems.

http://www.gizmodo.co.uk/2017/12/apple-is-reportedly-preparing-a-way-to-unify-ma c-and-ios-apps/

The current state of Apple software development, which requires programmers to create separate macOS and iOS versions for each of Apple’s two platforms.