Does Grendel kill Wealtheow

No, Grendel does not kill Wealtheow, although he could easily do so. At first, he says killing her would be the "ultimate act of nihilism." But, later in the novel, he captures her, spreads her legs, and thinks about cooking the "ugly hole" between her legs. Eventually, Grendel decides that killing Wealtheow would be as meaningless as not killing her, so he lets her go.