(a) Iron rated 2.2 kW, 220 V:

Resistance: $R=\dfrac{V^2}{P}=\dfrac{(220)^2}{2200}=\dfrac{48400}{2200}=22\ \Omega$

(i) $R=22\ \Omega$ (assumed unchanged at the lower operating voltage)

(ii) At $110$ V: $I'=\dfrac{V'}{R}=\dfrac{110}{22}=5$ A; Power $P'=I'^2R=25\times22=550$ W

Heat in $10$ min $=600$ s: $$Q=P't=550\times600=3.3\times10^5\text{ J}$$

(b) $I=4.0$ A, $L=1$ m, $A=1.0\text{ mm}^2=1\times10^{-6}\text{ m}^2$, $V=2$ V

Resistance: $R=\dfrac{V}{I}=\dfrac{2}{4}=0.5\ \Omega$

Resistivity:

$$\rho=\frac{RA}{L}=\frac{0.5\times1\times10^{-6}}{1}=5\times10^{-7}\ \Omega\text{m}$$