When Grace came to Pete's room and he was packing, I think he was on the phone with Melanie Dorkus. We know she is going to be a big part of the finale somehow (the first part is named after her), so I think it will be because Pete is explaining to Grace about Melanie. I'm not sure if he's maybe related to her (sister? cousin?) or just friends or whatever, but he probably knows her. In fact, I think he may have been the Red Devil she saw after she was sprayed with the acid. That Red Devil didn't kill her (she is still alive -- Chanel said she sued the spray tan company), so I think it may have been Pete skulking around Kappa getting info for his "investigative journalism" and Melanie is his source and how he knows so much about Kappa (including the secret room with the bathtub and the tunnels).
As for why he's a murderer, I don't think he's a Red Devil killer, but I do think he was the Red Devil at the mall. I don't think he was planning on killing Chanel, just injuring her by shooting her in the arm (maybe hoping to scare her away so he could do away with sororities and fraternities or as a "revenge" for his friend Melanie?). However, he did have to kill the security guard so he didn't get killed himself. This is what he will explain to Grace and we will find out more about the Melanie situation, hence the name of the episode.