Did Noah's wife die in the flood?

Yes. And then she went to hell.

Allah citeth an example for those who disbelieve: the wife of Noah and the wife of Lot, who were under two of Our righteous slaves yet betrayed them so that they (the husbands) availed them naught against Allah and it was said (unto them): Enter the Fire along with those who enter. Quran 66:10

No. Allah saved all of Noah's family from the flood.

And Noah, when he cried of old, We heard his prayer and saved him and his household from the great affliction. 21:76

And Noah verily prayed unto Us, and gracious was the Hearer of his prayer. And We saved him and his household from the great distress, And made his seed the survivors. 37:75-77