On notifications if Google play services is not installed unless the app let's you configure another server to use in place notifications won't work that use Google Play services installed on the back end.
If sandboxed Google play services is installed, assure it has the neccisiary permission to run in the background (unrestricted battery and network) access. Not just the individual apps, but the google apps specifically as Graphene installs thegoogle stuff with standard permissions.
Same goes for apps that run in the background. If you expect them to be running in the background to auto update or perform another function then it needs to be permitted in the battery settings. Background updates may also rely on Google Play services.
Edit: to clarify I haven't experienced any issues myself that weren't directly related to my decision to not use sandboxes google play services (no push notifications) despite daily driving for years. It's a particularly old and reliable project in the privacy space, and while I'm sorry you experienced issues that doesn't make it an unstable project not ready as a daily driver (any more that somebody having issues with Windows/Linux makes those unstable and not ready to be daily driven).