Here’s how I approach this!
I think of system quality ratings as more like action ratings. That is, when you have a 0 in a particular action, you can still roll it in the usual way (2d6 keep lowest). If a system’s quality is brought below 0, then it’s disabled. What that means depends on the system. So Comms less than 0 means the computer systems are out, - ship sensors are out, communications are down, etc. Engines less than 0 basically means the ship can’t move, back-up power is offline, etc. Weapons less than 0 means the weapons are offline. Hull less than 0 probably means the ship has suffered some serious hull breaches and is now vacuum.
With respect to modules, I personally don’t apply damage to modules when the quality is reduced. The modules just operate at whatever the current quality is. For example, suppose a ship with Comms 2 has the Targeting Computer module. If the Comms system is brought from 2 to 0, I’d say the Targeting Computer would still work, it just would do so with a rating of 0. However, I think I might be willing to go along with damaging a module instead of reducing system quality, depending on the situation.
EDIT: While my house rules might be interesting, to answer your second question I think the intent of the book is that one of the modules is damaged when the system’s quality falls below the number of modules for that system. For example, suppose a ship has Comms 3 and has the Long Range Sensors and Nexus Link modules. If damage causes the Comms to be reduced to quality 2, my understanding is that no modules would be damage. However, if damage reduces the Comms to quality 1, then my understanding is that one of the modules would be damaged.