Equality of NSpace and coNSpace classes
I can't think of any counter-example for (i) right now. But (ii) and (iii) are true due to the Immerman–Szelepcsényi theorem[1], according to which $\text{NSPACE}(s(n)) = \text{co-NSPACE}(s(n))$ for all $s(n) \geq \log(n)$.

[1]: Wikipedia - Immerman–Szelepcsényi theorem