A small detail has to be noted, wether it has been recognized or not and claimed or not, a lot of rules give citizenship to people. The paperwork is about claiming it officially.
> If a child born to German parents acquires another citizenship at birth (e.g., based on place of birth [birth in jus-soli countries mostly of the Americas], or descent from one parent [one German parent and one foreign parent]).
In theory somebody could have two or three nationalities under that law (two parents and place of birth) but no more.
1. EU and associated countries (e.g. Switzerland)? Germany does not care
2. Other countries? Give reasons, get a permit.
3. German dual citizenship law does not make any statements how many citizenship you can have.
4. There are countries that do now allow citizens to renounce, e.g. Iran.
Say one parent is German and the other is British, and the child was born in Brazil. If the kid is entitled to Israeli citizenship under the Law of Return, they get to keep all four.