Is there any way to tell when the genitive will be -a and when it will be -u?
Thanks for the link. I will just memorize then. I thought there was a possibility that -u was just for partitive genitives, but that illusion is now dispelled.
"posiłak" is not a word, but I will assume that this was just a typo. But no, "Kobieta nie je posiłek" is not a correct sentence.
So basically, "jeść" (to eat) takes Accusative, which here is "posiłek". But it's negated. When a sentence using Accusative is negated, it takes Genitive instead. "posiłek" turns into "posiłku".
That is the only situation when negating the sentence changes the case. Other cases stay the same.
It is indeed incorrect. Unfortunately I have no idea how to edit a declension table. The Polish page is correct, though.