An NMOS amplifier with weird biasing

a): An answer:
b): An answer:
In the derivation already included is $v_{gs} = v_{in}$ . $\begin{array}{rcl} a_{v} & = \frac{v_{out}}{v_{in}} \\ v_{out} = R_{d} \cdot i_{Rd} \\ = R_{d} \cdot (- g_{m} v_{in} - \frac{v_{out} - v_{in}}{R_{g}}) \\ = \frac{- g_{m} R_{d} \cdot v_{in} + \frac{R_{d}}{R_{g}} v_{in}}{1 + \frac{R_{d}}{R_{g}}} \\ \Rightarrow \\ a_{v} & = \frac{\frac{R_{d}}{R_{g}} - g_{m} R_{d}}{1 + \frac{R_{d}}{R_{g}}} \\ = \frac{R_{d} (1 - g_{m} R_{g})}{R_{g} + R_{d}} \end{array}$
c): An answer:
$z_{out} = R_{g} ∕ ∕ R_{d}$
d): An answer:
$z_{out} = \frac{1}{g_{m}} ∕ ∕ R_{d}$