Neutral clerics (on the good-evil axis) are treated as good-aligned clerics for purposes of all turning rules.1)
It is always the alignment of the deity that determines whether the cleric turns or compels, not the alignment of the cleric. Depending on campaign setting, this might be the same alignment.
Turned undead move at their fastest possible speed, i.e. they flee.2) Attacking turned undead does not end the turn, but attacking compelled undead does end the compel. Turned undead keep their full AC, saves, and other defenses. They will do their best to not be hit, though they cannot attack themselves for the full 3d4 rounds.
Turned undead cannot move directly toward a cleric that turned them while the turning is in effect.3) Therefore, it is possible that turned undead could be cornered and find themselves unable to escape. If the cleric is in melee with the turned undead, the undead will certainly flee, prompting parting strike(s) (see Avoiding).
This is a roll that should be made privately by the DM. Players should not get to know how long their characters will be “safe”.
Turned undead can be continuously turned by the same cleric, until the cleric fails once. Every time turning succeeds, the DM rolls turning length privately. If the newly-rolled turning length is longer than the current remaining turning length, it replaces the current remaining turning length.
If undead of the same kind (e.g. skeleton) have multiple remaining turn lengths (due to being turned multiple times or by multiple clerics), the lowest remaining turning lengths should be replaced first.