Yes. See the deploying to your own server guide for more info.
Yes, you can use Deployd as a JSON API over HTTP.
Yes, Deployd is unopinionated on the front-end and you can use any libraries that you like. For frameworks that provide their own AJAX implementation (particularly Backbone), you should probably use the HTTP API rather than dpd.js in most cases. Dpd.js is still useful for realtime and user authentication, as most of those frameworks don't provide any built-in way to do this.
If you're interested, some of Deployd.com (such as the community page and the documentation's search feature) was built with AngularJS and certain parts of the Dashboard (such as the data and property editor) were built with Knockout.
Yes and no. Deployd is often compared to Meteor, since they are similar in several ways:
However, they are different in a few significant ways:
Deployd and Meteor solve many of the same problems in very different ways. You should try both frameworks to see which one better meets your needs.
In the future, the two frameworks may not be mutually exclusive. Deployd focuses on data management and business logic while Meteor focuses on front-end rendering in real time; it may be possible to integrate the two for the best of both worlds.