I would say that the eye is on Zelda's cloak is for the fact that her ancestor, OoT Zelda, disguised herself as a Sheikah to keep herself away from danger with Ganondorf. Since the deeds and things that previous ruler did go down in history, the next person in reign must symbolize their ancestors in some way. Since TP and OoT were so similar, it makes only sense that Zelda has the Shiekah eye on her cloak. For example, in ST, Zelda brought up Tetra. Tetra was ST Zelda's ancestor. So again, in some way she had to represent her. To represent her, she used her ancestor's blessings to move her spirit back into her body. With this, again, TP Zelda would have to represent OoT Zelda. Again, since the games were so similar (based upon the background info given in TP about the past), Zelda should represent the Shiekah and her ancestor, only for the fact that OoT Zelda disguised herself.
I'm just theorizing here, but maybe the fortune teller is possibly OoS Impa. She does have somewhat similar looks to OoS Impa. Her facial expression could be a little similar to Impa's. Her figure is definitely similar, which doesn't say much, but you could assume that the fortune teller descends from OoS Impa. I don't think the eye really has much to do with with the Sheikah though. There isn't much background information on the fortune teller anyway to assume that that eye is related to the Sheikah.
The wolf stone is something I never noticed with having the Sheikah eye. It's surprising to see that and I have an interesting theory here: If the stone has the Sheikah eye, it makes me wonder if the Skeleton that teaches you the sword skills is related to the Sheikah clan. I feel this way because of the fact that you're howling the song that's given to call upon your teacher. If he was related to the Sheikah clan, then that would explain the eye on the stone. But, then there's the fact that this:
the gossip stone, also has the eye on it. So that raises many questions for me. I don't think that I can elaborate on the stone theory much further, considering that TP isn't the only game that contains a stone with the Sheikah eye.
I really don't know how to explain this. They could be Sheikah, but again (referring to above), there is no way to tell if their background is related to the Sheikah clan. If they were related, then I would say that they'd wear the eye in representation, which they are doing. So, I think it's probably safe to say that they their background and ancestors are probably related to the sheikah clan.