I have add #include "Wire.h" in the sketch where I am using the library. This seems odd as I have already included it in the library itself.
The reason has to do with how the IDE decides what needs to be compiled. The sketch is scanned for include statements. Only the libraries referenced by the sketch as compiled/linked to.
This keeps you from creating a library that uses a library that uses a library that uses a library that the user of your library does not have. A quick glance at an example sketch shows all the libraries that yours is dependent on.
In the CPP-File I have to redefine this variable char _pExpAddBtns = 57; even though it is already in the H-File. Why is this?
You should not have needed to do that. Doing so is actually wrong. You need to define what happened that caused you to think you needed to do that, so we can help you resolve the issue properly.