If I had a fighter that was proficient with whips, could I equip a Kumade (which "doubles as a grappling hook") and take the feat "Hook Fighter" to "treat it as a two-handed melee weapon with 15-foot reach" (if I attach "at least 10 feet of rope or chain" to it) "that deals piercing damage equal to a heavy pick of its size and that has the disarm and trip special weapon features", including the x4 critical multiplier?
+If I can would I need to take weapon specialisation (kumade), (grappling hook) or (heavy pick) to increase its damage?
Is a grappling hook is not doubles as a grappling hook.
The Kumade can be used to attach to things to climb etc like a grappling hook.
Hook Fighter lets you use an actual grappling hook as an improvised weapon (although without the penalties) and gives it a number of special features. It doesn't apply to things that are not grappling hooks (such as the Kumade) at all.
I say it works by RAW, it says the Kumade can be used as a grappling hook and hook fighter adds to what a grappling hook can do.
Not sure why you would want to instead of just using a normal reach weapon that you wouldn't have to invest feats into though.