According to wikipedia's entry on Nayuki Minase (in the back there), romantic relationships between first cousins are not uncommon in Japan. Is this at all true?
Not uncommon in fiction. I think Japan is just as aware of the dnagers of first-cousin love as most of the rest of the world has been since 4 million bc.
Actually the last time I heard about a study, the results suggested that the increased risk of genetic defects in children of first cousins was negligible (vs. children of unrelated parents). Several states in the US (and not just in the deep south -- Colorado is actually one) allow first cousins to marry.
No studies I know on aunt/nephew or uncle/niece, but just self-insert as Kitagawa-kun or something and you can still have all the Akiko MILF fantasies you like. (mmmm...)