Am I right about this? (Animation Handler)

Alright, I'm using my own custom body for animation- don't I have to rename and add parts to the part of an Animation handler that has this in it for the animations to work?:

local Figure = script.Parent
local Torso = waitForChild(Figure, "Torso")
local RightShoulder = waitForChild(Torso, "Right Shoulder")
local LeftShoulder = waitForChild(Torso, "Left Shoulder")
local RightHip = waitForChild(Torso, "Right Hip")
local LeftHip = waitForChild(Torso, "Left Hip")
local Neck = waitForChild(Torso, "Neck")
local Humanoid = waitForChild(Figure, "Humanoid")

Also, am I right that each local figure is a part, and in the "()" is (Part0, "Then Part1")?

No it's what ever is inside the brackets is the Child of your Object that the function is waiting for.

-- ObjectParent:WaitForChild(ChildOfTheParent)
local Figure		= script.Parent
local Torso			= Figure:waitForChild("Torso")
local RightShoulder	= Torso:waitForChild("Right Shoulder")
local LeftShoulder	= Torso:waitForChild("Left Shoulder")
local RightHip		= Torso:waitForChild("Right Hip")
local LeftHip		= Torso:waitForChild("Left Hip")
local Neck			= Torso:waitForChild("Neck")
local Humanoid		= Figure:waitForChild("Humanoid")

If you would like for more help go to the ROBLOX Wiki