Not really Google's fault there. Ask Apple to allow background processes from more apps, and wait until that arrives, or start using an Android phone if you want to benefit from the "full" Google Now experience.
On Android, it's accessed much the same way as Siri and so is truly "Google Now" on that platform. On iOS, you made have to launch an app but I don't think it would make sense to change the name to "Google Very Fast" or similar. Perhaps the name also refers to the speed of getting information when you're already in the app.
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. When something Google Now finds relevant is available it creates a low priority notification that the user will see when checking the notification pane.