can i change/modify the app icon by app when it running?

First up, I moved your question to App Frameworks > Cocoa Touch because, while it’s not a great match, it’s much better than Xcode > Playgrounds.

Second, with regards your requirements:

i want make a specific Calendar app which can update date info in app icon, like iOS Calendar app

the answer is, no, there’s no way to do this. The Calendar app is built-in to iOS which has a special affordance for this feature.

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—
Quinn "The Eskimo!"
Apple Developer Relations, Developer Technical Support, Core OS/Hardware

let myEmail = "eskimo" + "1" + "@apple.com"

Let me add that it's always a good idea to file a bugreport not only for bugs but for enhancements or feature request also.

Dirk