Her name is Honoka. She's a part of Kazuki's circle of friends. In episode 6 of the first season she and a couple of other girls confront Yuzuki about her relationship with her brother. In episode 8 she leads Kazuki out from the card shop where they're playing together in order to confesses her feelings to him. When she's rejected, she tells him what people ...
Looks like my guess was right - "LRIG" is "girl" spelled backwards, not an acronym/initialism.
This was stated by KawaseP (a.k.a. Kouhei Kawase, one of the producers for selector infected WIXOSS) in an interview with Akiba-Souken (Ctrl+F for 作品要素).
──LRIGs are a distinctive part of the show, aren't they?
The LRIG character designs were done by [...
"-desushi" mean "becase" and "and".
Let's take a look at a few quotes from episode 5 for example.
Wow! This is a burning development!! Because Chiyori is Burning Chorizo!!
If Ruuko doesn't play, I'll play.
Because Chiyori want to play!
The word "-desushi" itself is normal ...
It is likely that by obtaining a new deck containing an LRIG, the mental effects of losing three battles are not an issue anymore.
This is based on the reasoning that Akira was physically scarred, with her mental scarring coming from the physical and Ulith, whereas Hitoe was mentally scarred - it is also possible (this, by the way, is just an assumption) ...
This is in accordance with Hanayo's statement that upon three losses, the Selector will lose her memories associated with being a Selector.
That is half true; Hitoe specifically lost her memories of being a Selector. Memory loss is not a consequence of losing three battles; the consequence is that the selector in question's wish becomes corrupted.
Some nice person added the track listing to VGMdb a little while back (I assume it's correct, though there are no scans of the listing included); here is a romanized / translated† version of it:
Battle ~ I can make your wish come true
doushite naite iru no? / "Why are you crying?"
fushigi / "Strange"
Chiyori / "Chiyori"
chiyoringaa, chiyorunbaa, chorisoo
The LRIGs came first.
In Season 2 episode 8 "This World is My Property" it is revealed that:
Quoted from the Selector WIXOSS wikia & confirmed from viewing the episode in question.
Also, from another Wikia entry:
In episode 11 of Selector Spread WIXOSS, There is a same-coloured battle:
It seems like when the selectors are battling with the same deck colour, they can choose who goes first.
This also ties into the real game - where there are no hard set rules on which player goes first. (although I presume this advantage is offset in some way)