Wait, how did Kaguya know what Eirin was thinking and that Eirin went to the shrine to curse Reisen?

Because aliens from the moon.
Or, alternatively, either Eirin said that last bit out loud or it was purely for comedic effect.
I'd prefer the first answer, myself.

You know those times when you can just tell what someone is thinking without them saying a word? it's like that.

Eirin said aloud that she was going to curse Udonge in the last panel of the previous comic.