The Purina feed is okay. It will make their poop stink to high heavens, but it will give them the protein they need. Here is an article that may help you find good feed. Buttons do have the same nutritional needs as coturnix.
https://www.backyardchickens.com/articles/what-to-feed-your-quail.79205/
I don't see any issue with the one with the white around the eye. It looks like normal markings to me.
https://www.backyardchickens.com/articles/what-to-feed-your-quail.79205/
I don't see any issue with the one with the white around the eye. It looks like normal markings to me.