Is React meant to replace Ember/Angular type of frameworks? Can React also connect with backend APIs to fetch JSON and present them on the frontend? I've been waiting to nosedive into Angular2 (when its out), is React a better alternative to get started with?

Yes, it's pretty much unnecessary to include React and a framework like Angular, Ember, or Knockout in the same project. And of course React works well with REST and GraphQL APIs for communicating with a backend. React is definitely a better alternative to a heavyweight framework like Angular for new projects.

As a relative newcomer jo JS frontend development, is there a canonical JS REST client library that works well with React / Flux, or do I have to write that myself?

Fetch is really easy to use, and is native in modern browsers. There are several polyfills as well. It eliminates the need for any libraries.

Fetch looks interesting but as far as I can tell, it's an in-progress standard with no support on any version of Safari or IE or any mobile browser whatsoever. Seems like it has a bit to go before it being 'native in modern browsers'

You can polyfill it in those browsers. Just use polyfill.io, or if you prefer, manually feature-detect it and if necessary load Github's fetch polyfill, which is good: https://github.com/github/fetch