Cats? Or Cat-Kneazle hybrids? The behaviour of Mrs Norris (snooping on students and Hagrid), Mrs Figgs cat (warning about Mundungus disapparating) and Crookshanks (recognising Scabbers and Snuffles) all seemed a bit Kneazleish to me.
Poor Filch, presumably he hoped he'd pick up magic by working at Hogwarts, but he is just frustrated and bitter at 12 year olds learning more magic than him, and he's fairly ineffectual at his job compared to a wizard or witch who could use spells to clean, tidy and repair stuff after the students. Though I suppose the house elves help.
He seems to use that magical mess remover, so not all wizarding products must require magic to activate.
At first I figured the Quick Spell thing could have just meant he didn't do well at school, rather than being completely unmagical but he does self identify as a squib.
I thought it unfair that Hagrid, after being vindicated over the reason for his expulsion didn't seem to get a new wand, and possibly magic lessons to make him a fully qualified wizard - though he did get to teach.
I think you are right that squibs could study some subjects and have jobs in the wizarding world, perhaps especially muggle studies and in muggle relations.
You'd have thought that witches and wizards from all magic families would have picked up more magic from their parents before they started school (even if they aren't allowed to use it outside school, presumably they would have heard the incantations etc).
And if its common to dress in muggle clothing in the summer holidays, attend muggle primaries and in their down time at Hogwarts (not sure the latter was true in the books) then why are adult witches and wizards so hapless at muggle dressing when necessary or are they just not keeping up with muggle fashions.
I think the children are either home educated or attend muggle primaries, I hadn't heard of wizarding ones.