Well, that Reader One (One Reader?) only seems to show the current top N posts of a couple of popular sites (Hacker News, Product Hunt, Reddit, Slashdot, Designer News, Lifehacker, ...). Is there a (hidden) feature to show the top posts on a daily, weekly or monthly level?

I don't think so. It's not my project either. It was featured months ago on product hunt and since then I didn't notice any update on the app.