what exactly does a zobel network do?

Here's a basic definition from: http://www.trueaudio.com/st_zobel.htm

A Zobel is a series resistor-capacitor (R-C) network that is connected in parallel with a loudspeaker driver in order to neutralize the effects of the driver’s voice coil inductance L(e).

At least as I have seen it practiced with my Merlins, the Zoebel has to do with presenting a more uniform load to the amp.

Wikipedia says that: "Some loudspeaker crossover designs include Zobel networks wired across the tweeter (high frequency) driver to compensate for the rise in impedance at high frequencies due to the inductance of the voice coil. The goal is to try to keep the load seen by the crossover circuitry as resistive as possible."

Based on my conversations with Pass, the specs for the Zoebel need to come from the amp manufacturer not the speaker manufacturer (ie the speaker doesn't know its there, the amp does)

There is no apparent downside - try them in and out and use it the way it sounds best to you.

Zobel Resistor: for a driver with an impedance of 8,4,2 ohms, the values are 10,5,2.5 ohms respectively. For other values of driver resistance, follow the progression. Pay attention to color, it identifies the ohmic value.

Zobel Capacitor: find the voice coil inductance and divide by the zobel resistor squared.

The rest of the stuff is an easy google.