How is the authentication and authorization in my App managed?

Every app accesses the central configured Identity Provider in the server settings. By using the server action within process designer  a certain Identity Provider can be selected (per app).

Have i configure my external Identity Provider for every app built on simplifier?

No all identity provider can be centrally managed and over server action you can choose one or more for you business application.

How to check rights within the app?

You can use our User Business Object to read

combined with a condition you can hide fields via ui action or filter certain data.