1. On android if Google Play isn't available (or you install the no Google apk version) it'll use a websocket for notifications. Apple doesn't allow a persistent connection except through their own notification framework.
2. In either case Signal doesn't send message contents through the notification framework (not even encrypted). Once Signal receives a notification the app wakes up and reaches out to the signal service directly for actual encrypted message.
3. Regardless when signal shows the contents of your message in the notification menu of your device your device keeps a record on your device of that message content.
The FBI here didn't get anything from apple, once they had the apple device unlocked they looked at the notification database on the device to get the message contents. This isn't really any different from the fact that if the FBI has your unlocked phone they can read your signal messages. The notable bit is that the notification database retains messages even after the app is deleted.