So just watched episode 3 of season 2. So does this whole Reina arc mean that the reason by Reina killed Keichi in the old original series because she has been killing her dads hostess friend nearly every loop? If that's the case how was she getting injected with the sickness if Satako wasn't in charge of those original loops?
Regarding Rena attacking Keiichi, that was just about the Gou arc. In the original series, the correct answer was that Rena
wasn't trying to kill Keiichi. Keiichi was delirious by the end. He was the one succumbing to the syndrome and due to that saw Rena and Mion being much more sinister than they actually were, alongside seeing complete illusions a few times (the needle in the food, or the scene where Mion and Rena hold him, where it was meant to be a prank where they'd write on his shirt, but he saw it as them holding a syringe). This was revealed in the final story of the original season (if you go by the anime) or 2nd arc of Kai for the VN.
As far as Rina goes, the scenario where she appears and ends up killed by Rena could happen naturally too, without Satoko's intervention (yet again, it happens in the final story of season 1). Although that Rina was working alongside Teppei and was a worse person in general, attempting to attack Rena herself before she was killed, rather than talking with Rena about telling her father to stop seeking her. That scenario doesn't happen everytime though. In many worlds Rina ends up killed by the Sonozaki after trying to steal from them (this is what leads to Teppei's return to Hinamizawa in the old series).
Everyone in Hinamizawa is technically infected by the syndrome, but it only progresses if the character is under tension, leading to paranoia. In the original story for example, Keiichi's starts to progress because he leaves Hinamziwa for a while to visit a funeral, hearing Hanyuu's voice there somehow. Then returning to Hinamizawa he learned about the crimes during Watanagashi, but all his friends tried to hide them from him, which made him start suspecting them, escalating from there.
In Gou, it was suggested the syndrome weakened without Hanyuu around, which is why all the killings now seem to be artificially caused by Satoko injecting them directly.