It’s more the ‘furries are sexual perverts’ stuff that’s the lame retconning.
We were around for a long time before the media at large noticed us - and then it started out looking at the 'suiters and lifestylers. The yiffy stuff became the media’s focus a few years later, and that’s when the whole thing exploded.
I’m rather offended by the idea we should have to give up our terminology because the media decided to focus on one part of the fandom, rather than the people mis-informed by the media stepping back and realizing they’ve been misinformed.
Yes. 
Seriously, whether Nekomimi count depends on who you ask. I definitely count them as a kind of furry character, but not everybody they appeal to would necessarily be a furry fan - and there are some who would consider them not to be furry characters, being literally humans with animal bits stuck on.
Bunnygirls are usually of the Playboy Bunny type, and, IMO and IME, neither count as Furry characters, nor hold any special appeal - either intended or actual - for Furry fans. Though we’re no more or less effected by them than any other person.
Dunno. Maybe, maybe not. No real info to go on for that assessment, here.
To put it simply ‘just liking a cartoon’ makes you a fan of the cartoon.
Being a furry fan means being interested in the concept of anthropomorphic animals in general.
Just enjoying a series with anthro characters doesn’t put you in furry fandom.
Just liking many series with anthro characters doesn’t put you in furry fandom.
It’s liking them BECAUSE of the furry characters that marks you as a furry fan.
I’d never have read the Redwall books if they were just generic fantasy with humans and elves, but since it’s mice, badgers, and hares vs rats and stoats, it got my attention. That’s what marks me as a furry fan.