I think so. I don't know of many liquids whose surface tension is strong enough to resist a vacuum. Also, I've never heard anyone propose mercury (the metal) as a particularly good substrate for life.

Well, there's the possibility of liquid water under icy moons.

Only if it's exposed to vacuum (or an atmosphere). It might be enclosed by ice or other (preferably but not nessesarily transparent) material.

Even if the ocean is exposed, we now have the time it takes for 1. the planet to become tidally locked due to tidal forces, 2. the atmosphere to be stripped away, 3. the ocean to evaporate. That might be plenty of time for higher lifeforms to develop.