I would suggest taking a skim through Chapter 5 of Roy Fielding's dissertation[0] (where REST came from) to answer some of your questions.

As for "What do you mean stateless?", read this quote from the posted article:

> ...if the engine of application state (and hence the API) is not being driven by hypertext, then it cannot be RESTful and cannot be a REST API.

Why does he say this? Well, he was explicit about state in his dissertation[1]:

> ...each request from client to server must contain all of the information necessary to understand the request, and cannot take advantage of any stored context on the server. Session state is therefore kept entirely on the client

[0]: https://www.ics.uci.edu/~fielding/pubs/dissertation/rest_arc...

[1]: From Section 5.1.3 https://www.ics.uci.edu/~fielding/pubs/dissertation/rest_arc...