Full spider? Heavens no. Posessed by a spider spirit powerful enough to create webs. Probably that. It didn't look like a persona, and Peter still seems human enough so it is probably posession. Probably symbiotic posession instead of paracitic too, but that would be rude to ask.

"Then why are you capturing the ghouls instead of merely destroying their means of locomotion? I figured the spirit within you was the one who would do the feasting. You look...."

She tilts her head and ponders for a minute, "Like you prefer heated dog, wrapped in a specialty bread, and slathered by chili... Though, I do not know why they call it that since I have never seen one made of dog."

"As for friends. I had a friend once. Though I was told if someone tries to kill you, you simply must kill them back."