Yes, the magic circles in Umineko no Naku koro ni are very real. They are taken from the book "The Key of Solomon".
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Sorry, no. They do sell pencil pouches though!
When the cicadas cry or ひぐらしのなく頃に.
Hanyuu appears in Higurashi no naku koro ni Kai (season 2 of Higurashi) episode 6
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There aren't many (unfortunately), but I can recommend Yu-gi-oh zexal. I know yugioh is silly and is very childish, but like kami no puzzle, the plot and ideas of the anime slowly come out and turn out to be quite good. If you're not in for mainstream, you can watch Liar Game, umineko no naku koro ni(hella scary though), and paranoia agent.