That might be your definition, but it doesn’t have any connection to any actual definitions of social class which I suggest you research.
Not true. It's very close to the Marxist definition of working class, which encompasses anyone who sells their labour for their living, and doesn't own the means of production.
People who consider themselves middle class by virtue of their job rarely like Marx's definition, though.
Leaving Marx aside, class indicators are much more complex in the UK than what job you do. Your class is like a jigsaw made up of different parts - your parents' class, your upbringing, your level of education, the type of school you went to, the type of university you went to if applicable, your current job, your job history, your partner's class and job, where you live and what sort of accommodation you have. If there are enough pieces in the jigsaw to show a picture, you will fall into a particular class (although you may not have all the pieces).
I consider myself working class, although some elements of my situation and background could be considered middle-class, because overall I have more working class indicators than any other.