I'm in the process of learning Cython and I wasn't able to find a direct answer to this. Also please bear with me as my understanding of C is limited as of now. As far as I understand, with the cythonize command, .pyx files are converted to C, and are compiled to platform-specific libraries (.so / .pxd). My questions are:

If .pyx files are fully converted to C, does it mean that these generated extensions are no longer dependent on python runtime after compilation?

Assuming the same host architecture, can these generated extensions be loaded into other languages, eg. via Java's JNI? If so, are there any hello world examples on this?
Cython extensions are fully C, but they heavily use the Python C API. This means they can't be run independent of libpython (and usually the Python standard library). However it is possible to load libpython into other languages and then use a Cython extension. Also bear in mind that anything you import within Cython is not compiled but needs to be available for import.

I don't plan to answer this fully, but both ImageJ (in Java) and Julia do support Python interoperability layers and do Cython extensions would work there. You're much better off searching for "Python-Java interoperability layer" than trying to create your own way of using Cython specifically.
Can Cython compiled .so extensions be imported into other languages, eg. Java?