"Nerede" is in the locative case (where things are), and "nereye" is in the dative (where they're going). If the sentence were "where are the scissors," you'd ask "makas nerede?" But once you talk about "putting" something, it has a directional element: it's not just sitting somewhere; you moved it to somewhere. So "makası nereye koyduk" is basically asking, where did we take the scissors and move them to? (It's kind of a hard distinction to make and explain in English, I'm realizing. =) )
I used to be the difference between where and whither. Nereden would have been whence, I suppose. English speakers may still know these words from Shakespeare and the King James Bible.
Persze, de a magyar és a török két régi szomszéd.
Think of it as this: The word "to put" implies motion just like the word "to walk". That's the reason.
It's the ending of the verb.