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.
In 'Beowulf,' the warriors, who were witnessing Beowulf's battle with Grendel, attempted to help the warrior vanquish the monster by hacking away at Grendel with their weapons. However, the problem is that Grendel has a charm which protects him against weapons. As a result, it's through Beowulf's efforts alone, that Grendel is defeated.
I'm assuming you mean when!? he first encounters Grendel's mother after arriving in Denmark and killing Grendel he then tells the people of the town that he will kill it's mother. he comes back without the dragon horn (reward for killing Grendel) and tells everyone that he has killed Grendel's mother though he actually hasn't