Is this genetive singular? If so, why not the accusative, kobietę? Thanks
Yes it is singular, genitive. Because you need genitive after szukać.
(My interpretation - because NIE MA JEJ , and we need to JEJ SZUKAĆ,) - as you probably know negation usually needs genitive
What about "you are looking for that woman"?
As the Polish question didn't use 'czy' - yes, the indicative word order is also a good interpretation. Added now.
It's all right to but lady instead of women or not?
Well, "lady" is not a basic word, while "woman" and "kobieta" are totally basic...
Also, "lady" isn't even as popular as "pani" in Polish.