I recommend you to fix:

• First Script - Lines 1 & 2, line 10, & lines 14-16

• Second Script - Lines 5-8

FIRST SCRIPT

• Lines 1 & 2 - Local scripts are fast, because they run from the client (you). Because they are fast, this script will run before the local player is defined, so player will come up "nil". Because of this, character models may come up "nil" also (error for character model should show up in the output, unless this was tested in solo mode).

repeat
    wait()
until game.Players.LocalPlayer
Player = game.Players.LocalPlayer
Character = Player.Character
if not Character then
    Character = Player.CharacterAdded:wait() -- This is added to wait until the character model is not nil.
end

• Line 10 Optional - I'd use enumerations.

hole.FormFactor = Enum.FormFactor.Custom

• Lines 14-16 - I wouldn't name a variable as "script", because "script" by default is the running script itself. I'm not sure if the code will execute if you leave it as is. Rename it if you, too, are unsure.

local DamageScript = script.Script:Clone()
DamageScript.Parent = hole
DamageScript.Disabled  = false

SECOND SCRIPT

• Lines 7 & 8 - We don't know yet if the entity that touched the hole has arms/legs. A character model can still function without them.

local RightLeg = toucher.Parent:FindFirstChild("Right Leg")
if RightLeg then
    RightLeg.CanCollide = false
end
local LeftLeg = toucher.Parent:FindFirstChild("Left Leg")
if LeftLeg then
    LeftLeg.CanCollide = false
end

repeat
    wait()
until game.Players.LocalPlayer
Player = game.Players.LocalPlayer
Character = Player.Character
if not Character then
    Character = Player.CharacterAdded:wait()
end
Mouse = Player:GetMouse()

DamageScript = script.Script

Mouse.KeyDown:connect(function (key)
    key = key:lower()
    if key == "z" then
        local Torso = Character:FindFirstChild("Torso")
        local hole = Instance.new("Part", Character)
        local holemesh = Instance.new("CylinderMesh", hole)
        hole.FormFactor = Enum.FormFactor.Custom
        hole.Anchored = true
        hole.CanCollide = false
        hole.BrickColor = BrickColor.new("Really Black")
        local DamageScriptClone = DamageScript:Clone()
        DamageScriptClone.Parent = hole
        DamageScriptClone.Disabled = false
        game.Debris:AddItem(hole, 2)
        if Torso then
            Torso.Anchored = true
            for i = 1, 100 do
                hole.Size = Vector3.new(i, .2, i)
                hole.CFrame = Torso.CFrame * CFrame.new(0, -2.8, 0)
                wait(.025)
            end
            wait(.025)
            Torso.Anchored = false
        end

script.Parent.Touched:connect(function (hit)
    local Victim = hit and hit.Parent
    local Humanoid = Victim and Victim:FindFirstChild("Humanoid")
    if Humanoid then
        if Victim.Name ~= script.Parent.Parent.Name then
            local Torso = Victim:FindFirstChild("Torso")
            local RightLeg = Victim:FindFirstChild("Right Leg")
            local LeftLeg = Victim:FindFirstChild("Left Leg")
            if RightLeg then
                RightLeg.CanCollide = false
            end
            if LeftLeg then
                LeftLeg.CanCollide = false
            end
            if Torso then   
                Torso.Anchored = true
                Torso.CanCollide = false
                for i = 0, .5, .1 do
                    Torso.CFrame = Torso.CFrame * CFrame.new(0, -i, 0)
                    wait(.5)
                end
            end
            Humanoid.Health:TakeDamage(25)
        end
    end
end