Personally I use pretty much the same method as you stated but if I want it to clear out I usually do a cold crash for at least a couple days. It makes a big difference for me especially when I want to keg soon after a big dose of dry hops. :mug:
I'm no microbiologist but I think should definitely sanitize the cold steeped liquid before you add it to the fermenter. Myself I put it in a pot on the stove until it reaches 150° then put the lid on and let it cool. Essentially pasteurizing the liquid. You could boil it but you might loose...
I know a guy who regularly tops up his carboys with water from his garden hose without problems or at least he doesn't admit to it. So you should be just fine...
I imagine distilled water is quite sanitary right from the bottle anyways.
I've been using this method for over a year now and I really like the results. I find it gives me a rounder more rich character to the brews I use it in. When I used to mash my dark grains I always felt it had a bit of a harshness to it. Now I cold steep the day before a brew day than add it to...