Calculate voltage drop across Linear MOSFET in saturation region
The &quot;Input Admittance&quot; graph in Fig. 7 shows the relationship of V(gs)
and I(D) but there is no V(DS) listed.

\$V_{DS}\$ is held constant at 10 volts as per this statement: -

The symbol \$g_{fs}\$ (transconductance) is called input admittance in Fig. 7 but should be called transconductance. You'll get used to it! Anyway, the point I'm making is that the table above refers to transconductance (\$g_{fs}\$) and therefore \$V_{DS}\$ will also &quot;be held&quot; at 10 volts for the graphs.

I think I might be misunderstanding what the &quot;Output Characteristics&quot;
graph is showing. According to this article, that graph is showing the
voltage drop. But I don't understand how that graph is being read. Can
anyone explain that?


There are several gate-source voltage trajectories and when each gate-source voltage is applied, \$V_{DS}\$ is adjusted and drain current is recorded. The vertical line corresponding to \$V_{DS}\$ = 10 volts yields the admittance graph in your first question above.

Does this mean that the RDS(on) is always the same for all V(gs) that
are above the threshold voltage?

RDS(on) is irrelevant for your particular application but, if you want an answer, it's the inverse-slope of the above trajectories when drain current is 0.5 amps (as per the statement in the top picture). The slop is I/V therefore the inverse is V/I which is resistance.

why is it rated for P(D) = 960W?

If you look at the safe operating area graph you can see that it is capable of handling a power of 960 watts if the case temperature is held at 25 degC (harder than you think): -

Approximate estimations: -

red circle = 250 volts x 4 amps = 1000 watts
purple circle = 100 volts x 10 amps = 1000 watts
blue circle = 30 volts x 30 amps = 900 watts
green circle = 10 volts x 100 amps = 1000 watts

Never get close to these levels in practice except for very short periods of time.

PS, I'm glad to see that you took on board some of my simplified circuit recommendations: -

But you really do need to use the RC network around the op-amp!