Can you make addons with languages other than Python?
No, not without a different API. There really isn’t a more appropriate language to author addons in anyway.
There are ways of writing performance sensitive code in C and C++ and executing with Python, but the interface between Blender and that code will still be the Python API.
It is possible but you will still need to minimally interface with Blender and that part has to be done with Python. For instance you can write a mesh processing application in C# that interfaces with Blender over sockets, and that sockets part needs to be done in Python.
Adding to that, its possible to make python extensions using C/C++/Cython