How would I go about fixing my key input animation script?

The problem is the way you are waiting for the character:-

local character = player.Character or player.Character:Added()

Added is not an event for a model, also we need to be using the player object: like so:-

local character = player.Character or player.CharacterAdded:wait()

We use the CharacterAdded and then the wait RBXScriptSignal. This will wait till the event is fired meaning we will have access to the character.

For this kind of task it would be best to use StarterCharacterScripts as we only need access to the players humanoid:-

-- This script will be in the players model 
local humanoid = script.Parent:WaitForChild("Humanoid")
local anim = Instance.new("Animation")
anim.AnimationId = "rbxassetid://511512134"

-- you should re-think this part as you do not need to pass the variable nor load the animation each time you press the key
local function playAnimation(Anim)
    local track = humanoid:LoadAnimation(Anim)
    track:Play()
end

game:GetService("UserInputService").InputBegan:connect(function(input ,proc)
	if input.KeyCode == Enum.KeyCode.F then
		print('ran2')
		playAnimation(anim)
	end
end)

It would also be best I you did not load the animation every time the player presses the f key, instead load it once then play the animation track when the key is pressed.

I hope this helps, please comment if you do not understand how / why this script works.