What makes you think that? Why do you think either of these are snippets?
For Yuyuko, Youmu says, Yuyuko says, blah blah blah. So, you can assume she also says other stuff that would be relevant to teaching her. Like teaching her how to pour tea.
For Yukari, it was fairly clear that Yukari went to Youmu to tell her this information. Instead of straight up telling her, which she could have, she decided to teach her how to read the temperament.
According the the wiki Akyuu actually does say "[jinxes] are not like normal gods, but a kind of youkai."
Yeah, if you only read that sentence. But what she says is:
Although jinxes are a kind of god, they do not seek faith. They are not like normal gods, but a kind of youkai. It sounds to me like Akyuu states that Hina is a god, which she also mentioned earlier. Then, she went ahead and said they are not like normal gods, but a kind of youkai.
So, when you asked my take on it, I said, her nature is more like a youkai than a god, however, she is still a god.
For further explanation, gods normally require faith to subsist. However, unlike normal gods, jinxes do not require faith. And because of that, they are more like youkai than god. That said, it doesn't mean that they aren't gods. I don't believe Akyuu is saying that anywhere.
Fairly important question: Lily White (and by extension, Lily Black) aren't only present in spring, like Letty in winter and the Aki sisters in autumn?
Yes, they could be present in the other seasons. However, finding them is quite difficult.