"I do not see a woman here."
Translation:Nie widzę tu żadnej kobiety.
It is not – in fact, I would argue that it is better translation than the default. ;-)
edit: although, after second look, you should probably not put "Tu" at the beginning of the sentence – „Tutaj nie widzę kobiety” and „Nie widzę tu/tutaj kobiety” sound better I think.
Duo currently/still rejects
"Tutaj nie widzę kobiety"
and instead proposes
"Ja nie widzę tu kobiety."
Frankly, I disagree with the idea of calling "Tutaj nie widzę kobiety" a good translation. Sure, it's grammatical and so on, but putting "tutaj" at the beginning (and also at the end) gives an unusual emphasis. It's like "HERE I do not see a woman (but I do see women almost everywhere else".
So the rules I take away from here are:
1) "Tutaj" at the beginning or end of a sentence is OK if special emphasis is intended;
2) Elsewhere, "tu" and "tutaj" are interchangeable (though "tutaj" is safer for me because it looks less like the French for "ty");
3) In some cases, even native Polish speakers disagree amongst themselves ;-)
The original sentence contained "here", so you should not skip "tu/tutaj" in Polish either.
No you don't – „żadnej kobiety” would most naturally be translated as 'any woman' in this context and is accepted simply because 'a woman' can(through not always should, only if you need to stress that is some indefinite woman) be translated like that – Polish doesn't have articles, so in lieu of things like a/an and so on, we make do with demonstratives, determiners and pronouns. ;)
Yes. The only bigger difference is that 'tu' sounds rather clumsy at the end of the sentence, and we may not accept it. It's a bit like the emphatic/neutral distinction between some forms of pronouns.