These are great questions! I’m surprised that, for as long as this module has been available, no one has raised the topic before.
I’ve run the module a few times, but this encounter is always a challenge to referee. The meeting with the sphynx is not scripted, so as the GM you will need to improvise. Let me begin by setting up how I view the sphinx’s tent.
There’s an enclosed wagon that’s ostensibly used to transport the “sphinx”. I stress that it is enclosed, so there’s no way to casually look inside between the acts. There’s a heavy door in the back of the wagon with a strong lock. It opens into a cage that is assembled from 10x10 panels of bars that are secured together by chains and locks. If that sounds strange, remember the whole operation needs to be portable. The cage is secured tightly to the wagon and held in place by large stakes driven into the earth. The dirt floor inside the cage is covered with exotic looking rugs and large cushions. This whole affair is inside of a large tent that is itself inside the menagerie bigtop. Around the inside perimeter of the sphinx’s tent is hung a curtain, close to the outer panel of the tent, with just enough space for Ika to skulk around using her illusion magic unobserved. Also, there is a rope creating a partition between the cage and where the audience stands, to keep them at a distance in case the sphinx tries to lash out at a cheeky spectator. The light level is dim inside the tent.
When it is time for the sphinx’s performance, the guards within the tent first go over the rules—kind of like what Dr. Chilton said when Clarice Starling went to meet Hannibal Lecter for the first time. They are trying to ratchet up the suspense—it’s all part of the showmanship. It’s also an effort to prevent anyone from interacting with the illusion. After the “safety lecture”, one of the guards uses a hooked pole to reach into the cage, lift the bar from the door and swing door open. Ika has her spells up and out comes Jherizhana. Now we finally get to the questions…
What does the Sphinx actually do to be considered an attraction? I don’t mean to be immature, but turn to page 7 in the module and tell me if you see anything the 13 – 99 year old male demographic would pay to see. That won’t get you very far at a PFS table, but honestly I think that’s the motive for most of the townies. OK, for real now, at first she paces around the cage without speaking, meeting the gaze of each spectator, looking for weakness. She’ll select the boldest one and begin to interview him/her. “So. Do you like what you see? Am I everything you paid for?” You could play her off as either mocking or self-pitying. She will ask the PCs questions about where they are from and why they have visited the carnival. If they performed very well (or very badly) against the “baby dragon” she will also compliment (or belittle) the pertinent PCs. If asked how she knows what happened, she’ll just say that word spreads quick in the carnival.
If asked about herself, she will describe her homeland in the desert of northern Garund. Often players have asked her if she is being held by the carnival against her will. This is a touchy subject. If the PCs think of her as a slave, they may act to free her. To counter this, she’ll describe how she’d love to rip her captors to pieces if she escapes. Their families too. She may be sentient, but never doubt she’s a maneater. To impress this upon the players, after they’re going back-and-forth for a bit she might ask if they want her to read their palm. She’ll ask them to step closer, at which point the guards will intervene to “protect” the PC from losing a limb. She will try to act innocent, but everyone can see her stifle a sly smile if the ploy almost worked.
Remember, she’s an attraction. If there’s no menace, people will lose interest. She can’t be docile and innocent. Yes, this can lead the players down the path to immediately believe the carnival is behind the whole plot and the sphinx is guilty. Good! This is why the Guilded Hands targeted her. The longer the PCs have doubts, the more interesting the mystery is. If they metagame from the beginning, it kills much of the role-play opportunity.
Another thing you can have the sphynx do is tell the PCs their fortunes. It helps to think ahead about a reading specific to each PC, they’re hard to come up with on the fly. As a last resort, grab a bunch of horoscopes out of the newspaper. They don’t need to be accurate, just mysterious and foreboding.
If they PCs get too pushy, suspicious, or discover Ika’s presence the guards will immediately end the performance and try to hustle everyone out before the illusion is broken. Otherwise, the sphynx will tire of the conversation after 30 minutes or so.
What happens if the players want to talk to the Sphinx outside of the normal schedule? It depends if they have the carnival’s permission. If they don’t get Almara’s blessing, they’ve have to sneak in or cause a diversion. Remember, the wagon is enclosed so it’s not as simple as peering through a window. The PCs would have to get into the cage (chained and locked) and then pick the lock on the door. However, they would be suspicious from the get-go because something that big would make noise when moving/breathing in a confined wagon. If they have Almara’s permission then Ika would be in place and the PCs could talk to a much more cooperative Jherizhana. The sphynx would explain that what she says is mostly an act, and that she’s actually treated quite well by the carnival folk. She’d do her best to assure the PCs that she was innocent of the murders.
What do the carnival people tell when asked what the Sphinx is doing when she's not on display? Pre-murders, she’s sleeping or plotting a way to escape her wagon and have revenge on the carnival. Post-murders, she’s outraged that she’s been falsely accused and has been demanding the chance to represent herself and face her accusers.