Makes sense - still it feels odd, coming from the “other side“. I wonder when this split happened.
About dieser/diese/dieses, that would be tento/tato/toto (this/that here).
Articles usually appear in the languages which (are starting to) lose inflection. Say, there is a Slavic language which had lost its cases and does have the articles now - Bulgarian
It's all a kind of ouroboros of languages - if something gets simplified, something else appears there
> ten/ta/to
are you sure it's not "that" (dies(e,es,er)) instead of "the"?
> Not sure what is different if the nějaká is left out.
I'd interpret it as "The woman asks for the way.", i.e., a particular person is contextually implied. Otherwise it doesn't make sense.
EDIT: alternately, it describes an abstract event of woman asking for directions. Putting it as "paní se ptá na cestu" would make perfect sense in, say, a movie script.
Say a friend observed you from the other side of the street talking with her, approached you and asked what was that about.
You could say "[nějaká] paní se ptá na cestu" both with and without "nějaká". WITH "nějaká" you'd be emphasizing it was a random woman. WITHOUT "nějaká" it'd be that particular woman he saw you talking with. though, I'd use "she" for describing the event, i.e., "she asked for the way".