is noted that Grendel’s mother also lived in a similar abode as her child. She resided in the swamps not so far from Herot and it was there she fought with Beowulf to her death.

The history of the monsters suggests that they were the children of Cain in the Bible story. The monsters were condemned to live in the wastelands and as told in the story, both Grendel and the mother lived isolated in marshes or swamps.

This is actually sort of a difficult question because the origins of the words used to describe Grendel's home are unclear in the old texts.  Translated, the text says something like this...Grendel is:

"in moorland living," (from chapter one)

A moorland is a land full of moors, which is sort of like a boggy, scraggly, inhospitable place.  There is reference to "Grendel's Mere", "Grendel's Pit" and "Grendel's Peck" in the Anglo-Saxon Chronicle.  These would lead the reader to believe that Grendel is living in some kind of underground pit, watery cave, or nasty hole within a swamp, though it never really says.  It's a safe bet, though...Grendel's mother does indeed live in some kind of underwater cave in the swamp, so this probably would support the idea that Grendel lived in one too.

I would like to focus on the origins portion of this question. Grendel is one of the monsters that Beowulf must fight in this poem. Grendel is portrayed as a demon-possessed monster of sorts that eats people. He is a creature that loves violence for nothing more than the sake of loving violence and destruction. He repeatedly attacks Hrothgar's mead-hall night after night. When I first read Beowulf, I thought Grendel was a real monster complete with glowing red eyes, horns on his head, and massive claws. I figured there was a tail involved too; however, I think that initial assumption is wrong. The poem does give readers information regarding Grendel's origins. He is said to be a descendant of Cain.

Grendel, who haunted the moors, the wild Marshes, and made his home in a hell Not hell but earth. He was spawned in that slime, Conceived by a pair of those monsters born Of Cain, murderous creatures banished By God, punished forever for the crime Of Abel's death.

The Cain reference is Biblical. Cain is the brother of Abel, and Cain is guilty of fratricide. Cain killed his brother, and God banished Cain as punishment. The story states that Cain's descendants would bear his mark. Scripture isn't clear about what that mark is, but it clearly makes Cain identifiable. Grendel is Cain's descendant and/or a member of Cain's tribe. Because of that, I believe Grendel is human.

For twelve years, before encountering Beowulf, the monster Grendel had been embroiled in a war with humans. Before that, as a young monster, Grendel lived in a cave in a marsh with his mother who gave up language long ago. Their cave is at the edge of civilization but Grendel swims a lake of firesnakes and, on the other side, encounters the human world. Being a nearly immortal monster, Grendel watches the historic parade of mankind as it grows and changes and Hrothgar of the Danes becomes king.

The words in the original manuscript that describe Grendel and his mother are variations on roots used to mean wolf. According to linguists, wolf has the meaning of an animal and a second meaning on an outlaw who has committed a crime of such a nature that it puts the individual beyond forgiveness or redemption. A second root has the meaning of demon. Both these together paint the picture of Grendel as an outlaw with an animal nature who is a nearly immortal demon.

For more information on the linguistics pertaining to Grendel, read Grendel on monstropedia.org