Is the damage simply split up evenly if a hit falls within 2 or more subsystem radii?
No, only the closest system takes damage.
How do components play into this? Are they damaged randomly at certain specific subsystem health levels, and does repairing them restore that lost health?
Actually, it's more complex than that. Are you sure you want the full details?
First of all, if the system is powered off, it only takes 10% of the damage that would normally be applied. The other 90% is simply discarded, it is not sent back to the hull armor or any other system.
Second, different types of weapons may have different damage effects. Power draining weapons do not cause component damage to any system, but they temporarily drain power from
every ship system on the target, regardless of range and hull protection. EMP weapons cause power upsets, and will damage the closest power-critical system (usually a computer of some sort) even if the hit is outside of the system's radius.
For normal damage, if the damage level to be applied to the selected system is less than fifty points, all of it is applied to a single component selected at random. If the damage is more than fifty points, it is divided in half and applied equally to two components selected at random.
Now, earlier I wrote that all systems have 100 hit points. That is really an oversimplification. Systems don't have hit points at all, they have functional statuses for availablility, safety, and stability. Each of these statuses are expressed as percentages from an ideal rating of 100 percent.
Systems are made of components, each of which also has an availability that is expressed as a percentage from 0 (destroyed) to 100 (nominal). Each component contributes to the overall functionality of the system in different ways. Some components are primarily for safety (e.g. Radiation Shielding) while others are for stability (e.g. Power Regulator). Still other components may contribute in more than one way (e.g. the Plasma Impeller in a Plasma Drive contributes both to efficiency and stability of the system).
When a component is damaged or repaired, the functional level of the system is re-calculated in each of these three areas by multiplying together the availability of all of the components that affect the system in a certain way. If a system has four components that contribute to safety, and one of those components is damage to 50% availability, then the overall safety level of the system is (1 * 1 * 1 * 0.5) = 50%. If two such components are damaged to the same extent, the safety level of the system will drop to 25%.
The red/yellow/green colors on the caution and warning panel show the overall availability of the system. If the radiation shield on the fusion reactor has been damaged, the availability of the system will still display as 100% - at least for a while. Because the radiation shield is a safety component, the maximum safe operating level of the system will go down when it is damaged. If you continue to run the reactor at 100% power, it will eventually damage itself due to the radiation leaks. Likewise, if a power supply becomes unstable, it will cause power spike damage to any computer system attached to it.
When you repair a component using the engineering screen, or when the ship's engineer repairs it automatically, the availability of the component goes up according to the type of repair performed. If the component is replaced from spares, it is restored to like new functionality. If no spare part is available, the component can be repaired and reinstalled. Repairing a component will restore up to fifty percent of its functionality. However, if the component was severely damaged, attempting to repair it will lower the overall safety and reliability of the system by five percent each time.