Japanese speakers may remember numbers by taking the prominent syllable from how they read numbers (語呂合わせ goroawase). There are more than one way on how to count: one that descended from Old Japanese (大和言葉 Yamato kotoba) and one borrowed from Chinese (漢語 kango). In the order of Yamato / Kango:
ひとつ hitotsu / いち ichi
ふたつ futatsu / に ni
みっつ mittsu / さん san
Those are called floater, you know the thing that look like worm and when you move your eyes they also move away (usually done by a kid or childish person, they're chasing the floater). They look like this
Kamineko, 「噛み猫」 translates roughly as "Biting Cat", or "Evil Cat".
As far as I can tell, the only real role for Kamineko is the running gag, so I'm pretty sure he's just a jerk.
Perhaps he can sense Sakaki's allegies to cats and that's somehow a trigger, seeing as he seems to single her out from the other girls to bite.
The interpretation for the second 6 is probably a special case. The only reasoning that makes sense to me is:
ら is the 6th note in the Fixed Do key notation (C, D, E, F, G, A, B / Do, Re, Mi, Fa, So, La, Ti).
In hiragana, ら, also resembles the "5" or "6" number.
Please note that since it's a play on words, there're many ways to make the numbers work, just ...
It's from Episode 13, "Tactics without Guard / S / Midterms / Formation / Ability", specifically the Midterms / Formation portion.
Even more specifically, it's the 'Idiots' / 'Numbnuts' / 'Bonkuras' formation discussed when comparing midterm grades to the others (where their combined scores add up to 103, but Chiyo's and Yomi's are of course much higher).
As of this answer, Yen Press has not released the redone release of the series in either the UK or the US. They did however release the Omnibus, but that was before the 10th Anniversary of the series (and release of the manga, also why Yotsuba& went on hiatus).
The entire series was re-released as 3 volumes (one for each year), The author redrew a ...
According to the Azumanga Daioh wiki (revision permalink),
Chiyo-chichi ("Chiyo-Dad" 「ちよ父」"Chiyo-chichi"), is a strange yellow cat like creature...
According to Wikipedia (revision permalink),
"Chiyo-Father" (「ちよ父」 "Chiyo-chichi") is a strange-looking and even stranger-acting cat-like creature...
According to TVTropes, Chiyo's father is one example ...
The whereabouts and identity of Chiyo's real father, (and mother for that matter) are unknown. (It shown in the anime that they are alive, and in the manga Chiyo is seen waking her parents up at her house, but they are never seen or heard)