I do not know if having multiple Damage Control Modules stack their bonuses and if they do, if it's a meaningful advantage. If you have none of them, any repair will take hours. If you have one, it is cut down to minutes. The improved and advanced versions offer a better bonus. The wiki is wrong when it states that "Usually that works out to some hours, although a very large number of modules could shorten this time considerably" because even a single module will cut down the repair time significantly. Considering how much space they take, it isn't practicable, in my opinion, to stack DC-modules.
Furthermore, the wiki article that you linked did not specify whether DC modules help with parasites. They are automatically repaired in any case, just by being in the hangar. I do not know whether the host ship Damage Control Rating affects that.
(the psuedocode is quoted from here)
The psuedo code is as follows:
Repair Chance = Round Down ((Increment Length in Seconds / Item Cost) x Highest Damage Control Rating*)
If Repair Chance > 1000 Then
Repair Done = True
Else
If Random Number(1000) <= Repair Chance Then
Repair Done = True
End
End
* This is usually the damage control rating of the ship. However, if the ship is in a hangar and the mothership has a higher damage control rating, then the damage control rating of the mothership is used. This could be used by fighters on a carrier or it could be a huge repair ship that takes full size ships into its internal hangar. In this case, the maintenance supplies of the mothership are used.
Since you insist: there's the Word of God on how the whole thing works.
Now that wasn't enough last time, so I just checked - and as expected they work exactly as Cargo Handling Systems do. Adding more systems (and in fact there's nothing preventing you from mixing the various grades) stacks the bonus additively, so all types of Damage Control are the same size (3HS = 150tons), the Improved version is twice the cost of the basic component for twice the effect, and the Advanced is three times as expensive as well as three times as effective. Therefore giving your ship a rating of 100 will cost 250BP (excluding whatever Engineering Spaces you have), no matter what combination of Damage Control components you use - all that will change is the tonnage consumed.
For carriers/repair ships: if a ship is in a hangar, its Damage Control Rating is compared to that of the mothership and the higher one is used (the Maintenance Supply Points consumed are taken from the ship whose rating gets used).
For time to repair components: the time taken is proportional to the cost of the component being fixed and inversely proportional to the Damage Control Rating (though there is also an element of random chance involved). So if two of your ships both need to fix the same standard engine, and ship A has a DCR of 20 while ship B has a DCR of 40, A will usually take twice as long to finish as B will. If they are both landed in a repair ship with a DCR of 200 then (diceroll aside) they will finish at the same time - five times faster than B would on its own (and ten times faster for A).