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Yes, of course it can. Just not as oceans of surface water. Be that as it may even if water couldn't exist without the presence of atmoshpere your conclusion that extra terrestrial life could not exist is completely wrong. Venus and Earth have substantial atmospheres. Mars has a thin atmosphere. Jupiter, Saturn, Neptune and Uranus are planets of atmosphere. Even Titan, a moon of Saturn has an atmosphere You err in concluding that there is no 'air' on other worlds. There is on most, apparently. True, earth is the only one we know of where atmospheric chemistry, pressures and temperatures can support oceans of liquid surface water. But there may be Oceans of sub surface water on worlds within our ow solar system, not to mention the hundreds of planets known to exist around other stars. We don't know the conditions well enough on any of those other planets to say what their atmospheres are or if life as we know it could exist, but every thing we know about them suggests that our planetary system is not unusual. And the more 'typical' our home planet, and solar system is the more likely there is life out there.
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Can H2O exist without O2?
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Yes. Some of the moons of the bigger planets have been confirmed as having water, even though they have no atmosphere. As long as hydrogen and oxygen is available, and the gravity of a body is strong enough, water can exist, either as a gas (steam), liquid water, or solid (ice)
There are probably millions of planets that have both atmosphere and water to permit life on them. The chances of extra-terrestrial life is actually quite high.
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yes and no. without an atmosphere, liquid water will evaporate in an "effort" to create a vapor phase in equilibrium with the liquid (so will ice, actually, except that is called sublimation, not evaporation). If no atmosphere can be maintained, then the water exposed to the vacuum will vaporize into nothing with the passage of time (as long as there is enough heat in the system to allow it). Water can exist within the solid subsurface though where there is no vacuum to drive it into the gaseous state that will be whisked away into space.