Pike wasn't the only one keeping a straight focus. Andrea wasn't focusing on anything beyond exorcising the demon from Faith and Buffy getting out. Worry attempted to make her body and her mind rigid but she refused to let that leak through at the moment or else she would slip up, and neither Faith nor Pike could afford her slipping up in any of this. It, of course, was more easier said than done. Andrea recalled how having a demon inside of her had left Lois. It was a feeling that still left her uneasy and just more than a bit guilty for never noticing. Thinking of what would do to Faith just ... Let's just say if the demon hadn't been in her friend's body, she wouldn't have thought twice about ending it. The fact that she was going to help in sending it back to hell, helped her relax a bit, and filled her with a little bit of satisfaction. Though not by much.
Andrea glanced at the angel when he spoke but she didn't bother really acknowledging him beyond hearing his words ... and being grateful for his help. There would likely never be any trust for his kind but she wasn't so entirely against the entire race that she couldn't appreciate and realize what he was doing, and likely the risk he was putting himself in. It had her suspicious yeah, but it didn't mean she couldn't appreciate it, nevertheless.
Dean and Paige orbed in right after Cas had teleported his little group. It was Paige's iron grip on Dean that kept the anxious, hotheaded, Winchester from removing himself from her hold before the fully materialized from blue and white orbs into corporeal humans. Paige didn't know what would happen if a person tried to pull a way mid-orb. And she didn't want to have to explain to Sam or Buffy why parts of Dean was missing. Or something. She got his urgency but they were going to risk enough, they didn't have to risk it to impatience and mistakes.
Dean really didn't care who of this world was inside the building. He just wanted to know if Buffy was still alive and when they could go in and get her out. "How many demons are in the building?" Because Dean doubted that the Faith!Demon would just leave Buffy without guards to make things difficult for them.