OTC rubbing alcohol does, as you say, have quite a bit of water in it. But, the alcohol component does a very good job of evaporating the water away as the alcohol evaporates, so you end up with something that is a lot dryer a lot sooner than if you were simply to rinse it in water and shake it dry.
An easy experiment is to take two cotton balls, one wet with water, the other with alcohol, and wipe a streak down your mirror and watch the evaporation process. The alcohol streak, even with it being 30% water, will be dry a lot sooner.
As for blades, this isn't good just for DE blades; it's also recommended for the expensive cartridge razors.
As for storing alcohol, I always have a bottle on hand. I use it every morning to swab out my ears after I shower. If I don't I have problems with the water causing ear infections.