If a regular (not silent) push notification is sent to an app, and a user is not acting on it in any way, will the app "know" about it? Or it has to be silent push?
"will the app "know" about it".
If you implement a notification service extension, then when the push is sent to the app it can be intercepted by the notification extension. Note that the push will be delivered to the extension and not to the app, the extension and the app are separate entities. The extension cannot launch the app or call code in the app etc. However the extension itself can perform various functionality, run code etc. on behalf of the app.
The app and the extension can share files/databases/user preferences etc. So the extension could, for example save the content of the push payload to a database, then next time the app runs it could examine the database and thus know that a push was received and extract the data saved by the extension.