Last time I checked Lux didn't have many problems kiting. Slow, shield, bind all work together like a charm. The sitting duck complaint is valid with her, but that's kind of part of champion variety. Some people like playing a classic nuker that forces them to manage their offensive cooldowns.
Second... basically every mage loves CDR, although not all of them have it as their chief priority. If you as a mage have a low cooldown skill and your name is not Cassiopeia, CDR translates directly into DPS.
The signature spell thing is kind of iffy, because the Q is usually not what makes the champion unique. Breakdown:
Lissandra: Nope. Nope nope nope
Karma: Most powerful ability, but the shield bomb is her iconic thing
Elise: Nope - she's a spider. Q's a big tool for her, but she'd still be a giant damn spider with spiderlings without it
Syndra: Sort of. Her entire kit and sphere usage is her calling card
Diana: Yes, sort of - it's her calling card visually, but mechanically it doesn't do a whole lot (apart from preventing Akali levels of derp)
Zyra: Nope, it's her plants
Ziggs: The bomb is pretty Ziggs, but I'd say E is even more uniquely Ziggs
Viktor: Nope, it's his innate
Ahri: Nope - all three other abilities are probably more iconic and more central to her playstyle
Xerath: Nope, it's his W
And because it's actually fun, let's put the other champions in here too! (Tagged mage by riot.)
Anivia: Somewhat, but her entire kit is iconic (if that makes sense)
Annie: Nope. Tibbers and Pyromania are what you're looking for
Brand: W and R come to mind far faster, and how his innate works makes him what he is
Cassiopeia: Again... this is a case where the entire kit is iconic, the whole poison dynamic around her Q+E.
Cho: Rupture is a large part of Cho. Feast is even larger.
Fiddlesticks: CAWCAWCAWCAWCAW
Heimerdinger: Yes. But his Q is hardly a skillshot.
LeBlanc: Designed around Mimic, but Sigil of Silence still is very central to her kit.
Malzahar: E probably has a more central presence. Q just doesn't take huge precedence over anything.
Kassadin: Null Sphere does a bunch, but Riftwalk more or less makes him into an entirely different character.
Karthus: I'd argue yes, because Requiem, while far more iconic, also is not the core of Karthus. Lay Waste, however, is.
Kennen: Kennen is designed around his passive, his Q is as generic as they come on its own.
Orianna: Another whole-kit argument - but Q does tie the whole kit together, so probably yes.
Rumble: Yes. Flamespitter is Rumble's centerpiece without doubt.
Ryze: These days, yes (and it's a hella generic calling card). Oh, the time when Ryze was centered around his E and R...
Swain: Probably not - it's the demon-bird form that makes Swain Swain, mechanically and thematically.
Veigar: Probably yes.
Vladimir: Yes.
Zilean: Arguably, yes.
Funnily enough, the days when Riot didn't have the strict adherence to their design guidelines, mages apparently had more iconic Qs. But not by much.