I'm really late to this conversation.  I never saw Murphy as Harry's mentor.  In the last few books she was (mostly) Harry's friend and moral compass.  I'm not saying I liked the way Jim wrote her in the last three or four books, that's just my general impression of what her character's role was.

My feeling is that several years ago; maybe as far back as Changes, Jim decided that Murphy had to go, and I'll get into why later.  (Not that I really know why, so I'm going to be really vague about that.)  So, it's not that Murphy could no longer keep up with Harry and that made her character superfluous to the story.  It's that Jim wanted Harry to go in a new direction; one that doesn't involve finding his soulmate, at least not at the present time within the overall story.  Of course, with that whole "die alone" motif being repeated, you have to wonder if Harry will ever find a permanent romantic partner. 

To get back on point, Jim wanted Harry to become permanently removed from his best friend, the women he loved and his (sometimes) moral compass so his new course will be more of a high wire act than it already was.  I think Jim crippled Murphy as a way for Harry to see her as someone who could no longer remain in the larger game he was playing and as a way to make her death more poignant.  Murphy taking out the Jotun when she really shouldn't have been on the battlefield makes it a better death; sort of, except for Rudolph.

I'm not saying it was a good decision for Jim to make.  Only time will tell us one way or the other.  Even with what I see as the character's flaws since Changes, Karrin Murphy was the every person or mortal point of view and I think there is some risk in Jim removing her.  Michael Carpenter is in no way a substitute for Murphy's point of view because he knows the supernatural world and many of the major players, and even some of the minor players within it.     

What's known:
A Walker is a powerful Outsider.
They are Outsider Knights.
There are almost certainly three. Mac has strongly implied there are three Walkers.
They are He Who Walks Behind, He Who Walks Before, and He Who Walks Beside.
Nemesis is singular. Nemesis is repeatedly referred to as "it," not they or them.
Names are important and guarded. We often know things not by their names, but by what they are called. For example, Harry has a fairy servant called Lacuna and another called Toot. We don't know either's Name. Hell, I'm called Bad Alias. That's certainly not my name.

So, HWWBeside is an Outsider Knight, which are known as Walkers, called Nemesis.

What I think on possession/infection by HWWBeside: They're the same thing. Subtle manipulation to out and out control are both forms of possession as I understand it from everything I've ever seen on possession.

@Griffyn612: How do you fit Harry's black magic corruption into your theory of black magic being an opening to infection? Was his corruption simply an opening that couldn't be used? I once thought that all black magic corruption could be nemfection, but I'm not sure that's possible anymore.