I bet i could guess most of it. Teemo is just being AP teemo, the usual deal.

Nautilus is probably running armor reds and yellows, mr per level glyphs and either armor or ms quints. Masteries i'd say it's 0/9/21 from the naming of the page. His build seems to be some version of the old gp/5 one from season 2, he'd probably just branch out into support items when it got into mid and late game.

I'd say they're just taking advantage of the "mess" that is soloq, going with a full ap duo when most bot lanes would rune for more armor than mr and not being accustomed to dealing with the mass of cc known as nautilus.

I wish Nadouku would weight in on this stuff, he's the triple diamond guy.