How do I make all the parts in game.Players.LocalPlayer.Character fire with the function "Freeze()"?

Firstly, KeyDown and Remove() are deprecated. Don't use them in your script. Use UserInputService or ContextActionService in place of KeyDown, and Destroy() in place of Remove(). Here is your code with some small fixes:

player = game.Players.LocalPlayer
char = player.Character
mouse = player:GetMouse()
--Parts
head = char:FindFirstChild("Head")
torso = char:FindFirstChild("Torso")
rleg = char:FindFirstChild("Right Leg")
lleg = char:FindFirstChild("Left Leg")
rarm = char:FindFirstChild("Right Arm")
larm = char:FindFirstChild("Left Arm")
--Functions
function Freeze(object)
    if object.Name ~= player.Name or object.Name ~= "Baseplate" then
        object:Destroy()
    end
end

game:GetService("UserInputService").InputBegan:connect(function(input, gameProcessedEvent) 
    if Input.KeyCode == Enum.KeyCode.F then
        for _, child in pairs(char:GetChildren()) do
            if child:IsA("BasePart") then
                child.Touched:connect(function(hit)
                            Freeze(hit)
                     end)
                    end
        end
    end
end)

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In addition to DepressionSensei's answer, if you intend to keep the functionality where pressing 'f' activates the Freeze ability, you should add a flag to make sure you don't :connect things multiple times (which would cause the Freeze function to run multiple times for each object the player comes into contact with). If you want to be able to stop the freeze ability (say by tapping 'f' again), you might do this (expanding on DepressionSensei's input function):

--Lines 1-16 here
local connections
game:GetService("UserInputService").InputBegan:connect(function(input, gameProcessedEvent) 
    if Input.KeyCode == Enum.KeyCode.F then
        if connections then --Disconnect ability
            for i = 1, #connections do
                connections[i]:disconnect()
            end
            connections = nil
        else --Connect ability
            connections = {}
            for _, child in pairs(char:GetChildren()) do
                if child:IsA("BasePart") then
                    table.insert(connections, child.Touched:connect(Freeze))
                end
            end
        end
    end
end)

Use a for loop. For example:

for i,v in pairs(game.Players.LocalPlayer.Character:GetChildren()) do
    v.Transparency = 1
end

Now do that in your script.