Where is the Python API docummentation? Can I use code editor auto completion with the Python API?

Yes, it is down. You can find your options here:

Krita Python Developer Tools can generate an autocomplete in theory? I say in theory cause I use KDevelop and it doesn’t fully support all autocomplete features, so I haven’t gotten a chance to test it. But it should work at least according to spec.

You can communicate between applications in same way any application, sockets, file watcher and etc.