I have no idea what you're talking about. Graphene is my daily driver. "Manual configuration" does not ring any bells. Google OS-level integration being "absent" is a core feature, not an annoyance.
The problem with Graphene is that some app publishers are absolute asshats, they think their app is "more secure" when they require the Google verification spiel, when it is the other way around.
Is the battery life better with Graphene?
I would say, similar. In theory it may be slightly worse, because you are not using play services to deliver notifications, but each app does their own fetching (I believe that's how it works), but you will also restrict apps more (due to e.g. being able to restrict network access), so the two sort of cancel out.
Yes unless the app offers Unified Push (like Molly vs Signal).
I see. Thanks for the feedback!