Filling the tanks with Earth-sourced water would mean Earth bacteria, tardigrades, etc. The bacteria that stuck to the side of the tank, instead of being pulled out with the water-fuel, would reproduce once the tank is refilled from extraterrestrial (sterile) ice & water sources.
Could this be a cheap and dirty way of kickstarting terraforming? By landing and taking off on a planet like Mars with this engine, the steam exhaust would contain some of the bacteria and other denizens of the tank, some of which could be anaerobic. And this mixture could easily be intentional. The engine's steam exhaust could condense into a cloud of bacteria, and even precipitate to the surface.
Or the space ship could just have a sticker on the water-fuel tank door that says: Only use (sterile) space ice. No planetary ice.
Space is pretty big, I don't think anyone's ever considered it a problem there.
And re: reproducing in the tank, the temperatures generated would absolutely sterilize everything that was coming out as propellant. You could shove a zoo in there, and it would come out as fine particulate mist of mostly water and maybe some small burnt carbon particulate matter.
There are probably easier ways of spreading bacteria than via clouds, but it's actually an interesting idea - the bacteria could be used as the condensation locus, and cause rain that brings them to the surface. Just do a pass through the upper atmosphere, farting the whole way...
Why not? It's not as if water is flammable, toxic, or highly corrosive - attributes most other fuel sources do have at least one of.
(*Note, I am not an engineer)
Good question! His story "The Martian Way" addresses this. I don't really want to spoil it from you, but basically: where you'd expect.
> Surely they weren't storing it as H20 on the ship?
Why not? It's stable, it's useful for other reasons, and when you've got free energy and easy propulsion, there's no reason not to. (There probably would be some issues with sloshing, actually, but he didn't get into it. Asimov wrote a lot of stories that could be considered Hard Science, but I don't think he'd consider himself an engineer.)