Solving DC Operating Point of Common Source Amp
I will try to help without giving too much away. I just took an analog IC design course last semester, so I'm all psyched up about this stuff. I hope that this does not come off as too academic...

In a common source FET amplifier, the input (gate) resistance is really really high, so the gate current is usually assumed to be zero. So the current through $R_G$ should be zero. 

Also, you should know that the drain current in a FET operating in the saturation region is given by

$$I_D = \frac {k&#39;} 2 \frac W L (V_{GS} - V_t)^2$$

Where $k&#39;=\mu_n C_{ox}$ and is related to process parameters. $\mu_n$ is electron mobility (in NMOS) and $C_{ox}$ is gate oxide capacitance. W and L are the width and length of the channel, respectively. So you have an expression relating drain current to gate-source voltage. And $V_{ov}$ as well, since $V_{ov}=V_{GS}-V_t$.

You already know the drain current, $I_D=1m\text{A}$.

You also should know that in a common source amplifier, the open circuit voltage gain $A_v$ is related to the drain and source resistances, $R_D$ and $R_S$.

And you know that $V_{GS}$ should be equal to the voltage across $R_S$. (And you know the current through $R_S$, which is $I_D$. Correction: $V_{GS}$ is not the drop across $R_S$! But you should be able to determine the relationship from the information you have.

Without having a circuit drawing in front of me, and without having thought about it too much (please check my work!), I think that should give you enough info to make these calculations. You may have to leave in a "transconductance" parameter in the expressions for things if you do not know $k&#39;$ or $\frac W L$.

Analysis and Design of Analog Integrated Circuits by Paul R. Gray and Robert G. Meyer et. al is my go-to reference for transistor circuits. I have the 5th edition. It's been around forever. You would probably be okay with a 4th edition. I would highly recommend this if you are interested in linear transistor amplifiers (op amps).