What clientside routing system do you use inside the components? It seems there isn't one compatible with React and ReactNative. How do reuse functionalities between the two?
I highly recommend https://github.com/reactjs/react-router for building things on the web, where things are URL based. ReactNative has it's own router that's designed to work very well with the OS native navigations.
We're often not reusing functionality between the two because they're so different, and each platform deserves to feel native. Instead we're reusing the React components themselves which make up the app and UI logic of various screens.
What do you think of the "React Native Web" approach and consider the Web a rn platform?
This is a really interesting idea for future exploration and a lot of people on the team are experimenting with it. One serious missing piece is how layout is performed, on the web we don't have APIs to measure how text will layout, where we do have those things on iOS and Android native views. Starting to fill in those blanks over time by working closely with browser vendors and standards committees will help us explore this.