Some of brown dwarfs generate the enought amount of heat to warm their atmosphere up to 300 K. This is a condition to liquid water and, possibly, organic life forms.
Is where are a some studies about life forms in BD atmosphere?
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Although you might think that Y-dwarfs (brown dwarfs with temperatures $<500$ K) might become cool enough to support liquid water. In fact that does not happen. As discussed by Burrows et al. (2003) and Morley et al. (2014), in Y-dwarf atmospheres, when the temperature becomes low enough for water to condense out of the gas phase ($<375$K), it goes straight to water ice particles.
Thus, although water vapour will condense in clouds in a cold brown dwarf, it will be in the form of ice particles, and there is not expected to be liquid water in a brown dwarf atmosphere.
No. It would be really hard because although the coolest Brown dwarfs might be able to sustain water, they are made nearly completely of gas and that might by a problem. It would be very hard for water to exist on a brown dwarf, because if you were in the BD's "surface" the water would probably be in a gas phase due to the brown dwarf's low density there and pressure. But if it could exist as a pressurized water it probably still would be extremely hot, and unless the life form could survive that kind of temperatures it wouldn't exist.
Also, this is also very similar to life in gas giants. If it was to exist, it would need to be very small and not very dense. That way, it could still be part of the gases in the atmosphere and not sink.