Daylight should overpower darkness and cancel it out. I haven't had the chance to test this in game.
not magical darkness, no.
Dispel Magic maybe, but that probably would not work against an innate ability to create darkness.
As per the SRD
If any of this spell's area overlaps with an area of darkness created by a spell of 3rd level or lower, the spell that created the darkness is dispelled. Any innate ability should be no different than a spell unless somehow it is cast higher than 3rd level and the darkness created by Aksha should be dispelled by the 3rd level cleric spell Daylight.
Daylight cast and overlapping with Aksha's darkness did nothing for me in the game so to me this is bugged.