How does it work on Android? Does it use notifications there?

It uses a bunch of different kinds of interaction:

- A normal home screen widget

- A lock screen widget

- A special "drag up from the home button" gesture that can be triggered from any app

- Rich notifications. (As in you can trigger useful actions straight from the notification. E.g. for an event that's starting soon, you can email all participants.)

Yes, it puts some cards in the notification center on Android.

However, Android push is significantly more flexible than iOS push, if you push information to an iOS app, that information must appear as a notification, and the app can't process it until the user opens the notification.

Yes, but Android doesn't also have strict limitations of what an app can do in the background.

Yes. When something Google Now finds relevant is available it creates a low priority notification that the user will see when checking the notification pane.