1) Go to this page. Tells you details on how to register a Square Enix account. This is page for NA region, their is link at top for Europe. Helps to read this XD
2) You can download the client here.
3) I'm not at this point yet, but you need a "key" to actually get into Open beta (I always assumed keys = closed beta, think they lack the concept of what OPEN beta means)
Enjoy
~Pearz