Yes, I'm assuming that no circle is a square, and therefore a circle is a "not-square", and vice versa. Perhaps it's because I've led a sheltered Euclidian life, but I believe that assumption to be true.
Yes; you've made that assumption, but Mathematics isn't done on assumptions alone; it relies on definitions, axioms, and proven theorems (and a few Postulates, but those are stipulated as being deniable.)
I think your on the right track, though. Examine your premises, Grasshopper...... there might be an exception.