This is where you can ask questions about Golarion, the official Pathfinder campaign setting, including questions on rules and content for Adventure Paths, Campaign Setting books, Player Companions, and Modules.
Limp lash suffers a bit from using game terms as general descriptive text. Here are some clarifications.
1. You strike the target with the whip, he start taking ability penalties, is he paralyzed or hindered in any other way?
He is not paralyzed until the ability penalty reduces the victim's effective Strength, Dexterity, or Constitution to 1 (the minimum to which this spell can adjust a score). Once one of these 3 scores is reduced to 1, the victim becomes paralyzed—he is not paralyzed before this point.
2. The whip has a maximum range of 20 ft. If the target is not paralyzed or otherwise prevented from moving, what happens when he moves out of the 20 ft range? The spell dissipates or ?
If the target moves out of range, the spell ends. (This is similar to what happens if you let go of the whip.) This does mean it's relatively easy for a victim to escape from the spell—that is by design, since otherwise the fact that there's no save to resist the penalties is pretty powerful.
3. Can you take any actions while holding the whip?
You can take any action you want, but if any action requires you to release your hold on the whip, the limp lash spell immediately ends.
4. What happens if some effect attempts to displace the whip (e.g. wall of stone between you and the target), or some effect moves the target away (e.g. bull rush)?
The spell effect ends if something moves the target out of range or completely breaks the line of effect between you and the target.
Potion Glutton: The “Normal” line says that drinking potions is normally a move action. Isn’t it normally a standard action? And if so, the feat text seems to be based on the move action assumption, so what should I do?
Normally, drinking potions is a standard action, not a move action. To bring it in line with that, change the text of potion glutton to the following: “Benefit: You can drink potions, elixirs, or other potables (but not extracts) as a move action without provoking an attack of opportunity.
Normal: Drinking potions is a standard action that provokes an attack of opportunity.”
Sword Saint Samurai: The sword saint samurai’s brutal slash ability replaces an ability that doesn’t exist. What should it alter and replace?
The sword saint samurai’s brutal slash should replace the second sentence of weapon expertise with “At 3rd level, the samurai selects either the katana or the wakizashi.” This alters weapon expertise. Brutal slash also replaces mounted archer.
White-Haired Witch: The white-haired witch archetype says that it uses Intelligence instead of Strength for damage rolls, but does it still use Strength for attack rolls or does it use Intelligence for attack rolls like the hair hex? Can a tengu, nagaji, or other hairless character take the archetype?
A white-haired witch still uses her Strength modifier to determine her attack bonus with her hair. Witches of races that do not normally have hair can become white-haired witches, in which case, they supernaturally grow hair.