"...swipe and bring us"... means stealthily stealing and secretly carrying one of the Lunar stones Eirin has./The Kiteretsu Daihyakka is to the side of the Koujien on the shelf. In the original work, it appeared as a worn-out book which had no binding./Nitori-san is a bokukko.
I wish I had the chance to read Kiteretsu Daihyakka, there seems to be a lot of its reference in this series.
No, but I bet...So we can't?...but going by my boat may be a bit rough.We can reach the sea if we go along this river......you can swipe and bring us a Lunar flying stone.
飛行石 is probably a reference of the Levitation Stone in Laputa.Koujien
Probably the one mentioned in the commentary.