Just one of those nice little touches added to the game
Seriously though, I can′t remember if it did anything.
UESP has info on everything.
http://www.uesp.net/wiki/Oblivion:A_Rusty_Key#A_Rusty_Key
I'm not sure I know what you mean by "passive" in this context. If you're talking about the Argonian water breathing ability, it's simply a special racial Constant Effect Water Breathing, FormID 00047AD6, which is functionally the same as a Water Breathing Enchantment.
I added the effect to a Bosmer to create my "Naiad" race.
Oh, I see. I haven't timed the blue (breath holding) part of the cycle, but I wouldn't be surprised if it was the same for everybody. The red (taking damage) duration is determined by your character's Health, I believe.
I believe Endurance affects the amount of time our characters can hold their breath underwater.
I'm not sure what the exact formula is but it's based on 4 + 0.3x your Endurance. So at 30 endurance you could stay under water for 5 seconds. Does that sound right?