Major HBP spoilers. I don't know why my theories always end up being 'this person is actually this animal/bird/mollusc'. WELL, ACTUALLY, I DO. IT'S BECAUSE THOSE ARE THE TRUE ONES.
Crookshanks is James Potter.
Hey, he's always hanging around with Sirius, isn't he? And he launched himself at Scabbers in the petshop, because I don't expect he'd be too thrilled to see the person who got himself and his wife killed hanging around his son. That also had the advantage of drawing Hermione's attention to him, so she bought him and he had a means of staying close to Harry. And his face looks 'grumpy and oddly squashed', because THAT'S WHAT HAPPENS WHEN AN AVADA KEDAVRA SPELL, INSTEAD OF KILLING YOU, TURNS YOU INTO A CAT. DO NOT ARGUE WITH THE RIONA.
Okay, why is Dudley Hedwig? Well, I'm sure we've noticed the abusive relationship that Hedwig and Harry have. Oh, sure, they PRETEND to love each other, but she's always pecking him and digging her talons into his shoulder and being all huffy. Harry sometimes takes out his anger on her/yells at her for no good reason etc., because he is subconsciously aware of her being Dudley.
...well, okay, I don't have anything beyond that. And what I have could just be about a volatile boy and his touchy owl. LOOK A SHINY THING.
Ron's obviously the only one who actually KNOWS Dumbledore is the Giant Squid. He used to go out with the remarkably clingy Dumbledore, but refers to him only as 'the Giant Squid' in company, so as not to make his friends suspect. Hence his 'it's like going out with the Giant Squid' comment about Lavender.
The Giant Squid was only mentioned by Ron in Book 6 (understandable, as he's always half-thinking about the Squid/Dumbledore (by the slash I mean they're the same, not any kind of romance, although I could probably come up with a Squid/Dumbledore theory. Or maybe fic! (please do not hold me to this))). But the Squid never actually appears. This is because Dumbledore is too busy planning Harry's excursions into Exposition!Land, and also because, as he gets older and nears death, his squid-becoming powers begin to deteriorate. He worries that a transformation into the Squid will drain him of so much energy that he will die without being able to tell Harry about the Horcruxes.
Also, he knew that the Horcrux potion would make his transformation from mild-mannered Headmaster to Giant Squid uncontrollable, and also that his Squid form would be driven insane and attack the students. Unable to risk this, he had arranged prior to the excursion that Snape would have to kill him when he returned.
YOU SEE, IT ALL MAKES SENSE.