When a push notification is shown on the sleep screen, there is a time attached to it. What time is this? Is it when it was received on the phone?
Yes. All times listed on your phone indicate when you received the notification and are relative to the current time on the phone. This includes not only notifications on the lock screen, but also in the Messages.app, for example, and the Mail.app.
All time stamps are listed for when the notification was delivered, or when the action occurred on your phone (you made a phone call, and looked in Phone > History).