It's fascinating to see the differences. One side has flash cars, the other ordinary hatchbacks. One side is happy to wander around in a dressing gown during the day whilst the other is always smartly dressed. One side let their kids play in the street whilst the other has them in studying. One side is mostly trades people whilst the other works in offices.
Despite all the differences (or perhaps because of) it seems to work. I doubt either side would chose the situation but the fact the system forces them together is genius.
So to answer your point, no, everybody is not middle class.
I think "Working class" is a distinct thing from "Lower class."
At least here in the US, I know a fair number of people that would claim the label "Working class", though I doubt any of them would claim to be "Lower class."
"Working class" is a synonym for "Blue collar" to many people.
"Middle class" is less of a synonym for "White collar", but I think that distinction exists for some people.
You can't really do that for "traditional" definitions of upper class (which isn't based on anything as simple as having loads of money).
And anyway - everyone is middle class these days. Nobody claims to be working class and there are so few actually upper class people that most people will never meet one.