Yes, he may. But is unusual.
You should have sovereign counter or - if that too is too impressed - ignore the question skillfully.
It is not punishable but such questions are really inappropriate if you just knows the person zero. Of course he may ask and of course it is to decide whether you answer or not but everyone should be clear that such a behavior is really just inappropriate.
A question is not a criminal action (sexual harassment) and therefore not prohibited. But he should respect your answer or that you ignore him.
Yes, that's just a sign of poor education, but not punishable.
Everyone may ask you all. Whether you answer it is your thing.