"I do not see a woman."
Translation:Nie widzę kobiety.
I think this is wrong; "Nie widzę kobiety" is I do not see women. How is "Nie widzę kobietę" wrong?
You need genitive here, because you don't use accusative with negated verbs.
"Nie widzę kobietę" is a wrong case. Correct versions are: "Nie widzę kobiety." - I don't see a/the woman." or "Nie widzę kobiet." - "I don't see (the) women."
What is the difference between "Nie widzę kobiety" and "Nie widzi kobiety"?
Not entirely sure but I believe "Nie widzę kobiety." is for when you're speaking about yourself not seeing the woman whereas "Nie widzi kobiety." is for when you're speaking about another not seeing the woman. As in, "[Ja] nie widzę kobiety." - "I don't see the woman." and "[On/Ona] nie widzi kobiety" - "He/She doesn't see the woman."
A little EDIT to the previous post because the third gender is missing. "[Ono] nie widzi kobiety" - "It doesn't see the woman".