Why does Toki's foresight line up so neatly with mahjong turns? Because there's a branching point whenever Toki herself takes a turn. Seeing one turn ahead isn't just seeing "the future", it's seeing all the branching futures from every discard Toki could make. It increases exponentially from there. Three moves ahead requires foreseeing up to 1,728 distinct discard combinations, and there's the option of called melds on top of that.
In Saki Biyori, Ako gets a Yakuman tenpai on an Internet mahjong game while riding in Harue's car, only to lose connection. This is rare enough as is, but even more so for Ako, who typically quickly makes cheap hands, hence why she tries to get Harue to drive back.
Hiroko inferring that Saki and Teru are related makes quite a bit of sense when you consider that she's the niece of her school's coach, and cousin to that coach's daughters, who play for another school. It's thus natural for her to understand that when two mahjong players share the same family name, it's likely more than a coincidence, especially since her last name is different from that of Masae, Hiroe and Kinue Atago.
Kirame's cheerful attitude makes a lot of sense, when you consider that her ability is to not go under 0; in other words, she's always positive.
Assuming Kiyosumi makes it to the finals, Nodoka's opponent from Achiga in the vice-captain battle is not going to be any of her three friends (Shizu, Ako and Kuro), but Arata, who, at least prior to the tournament, has never met her and whom Nodoka most likely has never heard about. Even Yuu has most likely heard about Nodoka before (and Kuro's first line to Nodoka has her comparing Nodoka's breasts to Yuu, so Nodoka at the very least knows Kuro has a sister).
By the same token, if Kiyosumi makes it to the finals, Saki's opponent from Shiraitodai will be Awai, not Teru. Does that mean Saki's efforts are without meaning just because she didn't know in advance which position she'd need to be in to meet the person she wanted to meet? Most likely, just like Kiyosumi and pretty much every other school, Achiga's player order was decided based on which one of them was predicted to play best in which role (aside from Kuro, who probably got the vanguard position because, like Yuuki, she's the one who is least able to play off of her usual game).
The scene in which Saki talks with Koromo about Shizuno while watching her match with Awai would seem to indicate that Saki's aware of this, although one has to wonder how she's taking it.
