The series has ended, yes. There are 17 volumes (18 if you count the "Children" volume of character backstories that I believe was only released in Japan) containing a total of 99 chapters. As far as I can tell the atuhors haven't written any other manga.
Is there a reason so many of the character articles list their original/true/whatever names in their info boxes instead of the name they're commonly known by? For example, Ayanami's page has his Krowell Raggs name listed right there smack on the top of the infobox despite the fact that first of all, he's known as Ayanami throughout the series, and secondly, it's a big fat unmarked SPOILER. I'm inclined to go redo the pages to put the most common/primary name for a character at the top of their info box (to match the page name, essentially) and put all other names down in the aliases. Because it frankly makes a whole lot more sense that way.
Similarly there's a LOT of unfounded speculation and assumptions in various articles (Ayanami's and Verloren's in particular make me CRINGE when skimming through) but again, I hesitate to go through making sweeping changes since I don't know if there's support for the articles as they are or such.