In an archaic form it does.

But nowadays "Frau Doktor" usually refers to a woman who is a doctor, as "Doktor" has a male grammatical gender, so it's awkward to address a woman only as "Doktor X", even though that's technically acceptable. The grammatically female word "Doktorin" has not caught on, even though it's also correct.

There was no difference in German, it was "Herr Doktor" ("Mr Doctor") and you'd address his wife "Frau Doktor" ("Mrs Doctor"), so you couldn't tell who of them actually held the title (not sure what happened after divorce). Today, you need to get your own title, no more shared titles through marriage.

In Germany historically yes, but today most people mean the person him/herself.

It could be - just like how Mrs. Thomas Jefferson’s name was Martha and not Thomas.

A hundred and fifty years ago, yes.

Fifty years ago, could be either.

Nowadays, no.

This used to be true for English as well.