Hi Klime,
The REST API is actually the only way to communicate from a browser (or an other programming language) to the platform (and back).
And yes, the webapps are using Ajax (XHR actually, Ajax being a buzzword ;) )
JSON is, indeed, way easier to handle than XML (but historically, Ajax/XHR were based on XML).
I do not know the complete APIs, but their roles and features are tightly bound to their common usage and/or environment.
For instance, REST API calls have to be restrained to the minimum because they are much slower and also require more resources.
Cheers,
Valentin