It's broadcast at dinner time on Sundays. So yes, living in Japan one can hardly fail to know it. Character don't age. Technology is not really present, so it's kind of timeless.
Sazae herself is named after a shellfish. As are all the other main characters.
Sazae-san is such an institution here that there's slang describing the feeling when you watch it on Sunday night and know you have a full work week coming up: Sazae-san Syndrome.
That's interesting. Growing up in the UK as a child the equivalent of Sazae-san Syndrome was hearing the Antiques Roadshow theme. Even now when I hear that music it fills me with the Sunday night blues.
Everyone in Japan knows this animated show.
Yes! It's one of the few things I can watch and understand reliably in Japanese. It doesn't contain lots of slang or fantastical words.