As a side project, involving a Angular/Ionic/Cordova application and WordPress, I'm building a proxy plugin for the WP REST API in order to communicate securely with the API. The code is available on GitHub, should you wish to check it out. It's a personal project (currently running inside a Vagrant box) geared towards understanding the API and polishing my Angular/Ionic skillset and based on my limited understanding of the OAuth spec, so there's bound to be a lot of bugs and other issues.
But to answer your three questions:
- The REST API works behind a proxy;
- I'm using both plugins (REST API and API proxy) as a primary datasource;
- I'm not aware of any proxy services that work with the WP REST API, but a quick Google search lists some generic tutorials by Apigee and Amazon.
EDIT: I started working on my proxy attempt when version 1 of WP API was still in development and there are now several other authentication options, apart from Basic Auth and OAuth1. JWT based authentication seems to be a more streamlined option as opposed to a proxy. I'm currently experimenting with this JWT plugin developed for the API. Still uncertain about the security implications, though, as is this user. This provides an interesting, but rather bleak general overview.