Chlorine products are oxidizers.

They kill bacteria the way they destroy everything else -- by ripping into them, molecularly, stripping electrons off of the structures in their cell walls, and then ripping into enzymes and other molecules once inside the cell.

Sounds like fun, eh?

Bleach does effectively the same thing.

pH really doesn't factor into it... well, if the pH is too low or high (7-8 is good), then it slows down the reaction, but that's the only reason for it. It isn't really the pH that does the action, it's the oxidation that kills stuff.

As for Iodine... well... Chlorine products are not actually plain old chlorine. They usually break down in water to form some chlorate ion (there are four different ones) which really like to rip into other molecules, especially "hypochlorite". Iodine doesn't do nearly as effective a job at this, although I don't know exactly how good it could do it.

In any case, potassium Iodide is a completely different animal and is about as dangerous as table salt (note: too much of either can kill!). It's only molecular iodine, I2, which could form oxidizers and acids (so can molecular chlorine, Cl2) in water.