[Freakman]

About point 1 :

Spoiler for episode 2:

This comes from what I told you. Ooishi knows Keiichi hasn't been in the village long, and thus probably doesn't know/ doesn't care about Oyashirosama's curse, just like Ooishi says at the end ("I need the help of someone that doesn't believe in the curse")

Point 2 :

Spoiler for episode 3:

As you learn in episode 3, Takano was a nurse at Hinamizawa local hospital.
As such, from what I told in my previous post, it's no wonder she knows about Keiichi.