If Bridge Officer A has "Cannons: Rapid Fire I" and also has "Cannons: Rapid Fire II" what will happen with the cooldown? Is it shared? Is it as if I used both (yet only used one)?
If they're had by separate Bridge Officers (A has I and B has II) does that affect the cooldown at all?
I have two Officers (engineeniers) , one with engineering team I the other with engineering II.
They don't have the same cooldown, but you have to wait a little while before you can use the other skill ( like a smaller cooldown)
Each system has a shared cooldown, regardless of whether it is the same skill used or not. For example, "System: Cannon" has a shared cooldown. Using any power with this system will invoke a cooldown before another Cannon ability can be used. The shared cooldown is shorter than than the individual cooldown for each ability.
This is particularly noticeable with science abilities. For example, Polarize Hull and Hazard Emitters both use "System: Hazard". Using either one will invoke a shared cooldown which will prevent the other from being used for 10 seconds.