Ichika was Kippei's brother's fiancee. She got left behind when he ran away to travel the world and Kippei's mother tried to get her to marry Kippei instead when he came back to take over the inn.
I mean, I think it's a pretty common trope in shoujo/josei ("common" girl with an actor/singer/CEO/popular writer etc.), so if you browse those you'll find some. But I wouldn't expect most of them to be as chill as this one
My guess on the "godfinger" might be along the lines of "my finger was guided by the god and as such it was the god's finger that touched you" excuse, I think there was something like that in some movie/manga or something?