A error on "frame doesn't belong to screen Gui" How to fix?

To start, I recommend that, when posting your code, click on that "Lua Icon", above the area where you write your post, and put the code inside the set of "~" that just appeared, so it's easier to read your code.

About your error, what could've happened is that, you haven't waited until ChoiceFrame has loaded.

local choiceFrame = script.Parent.Parent.Parent:WaitForChild("ChoiceFrame")
local message = choiceFrame:WaitForChild("ConfirmationMessage") 

Small tip: I've noticed that your checking if the frames are visible, and if they are, set them to invisible:

if earth.Visible == true then 
	earth.Visible = false 
	if water.Visible == true then 
		water.Visible = false 
		if fire.Visible == true then 
			fire.Visible = false 
		end 
	end 
end

You really don't need to check if they're visible.

If they are visible, and set it to invisible, they will become invisible.

If they are invisible, and set it to invisible, then they will continue invisible.

This is just a small tip so you consume less time writing your code, and in the end, make a more efficient and clean code.

local button = script.Parent 
local name = script.Parent:WaitForChild("ElementName") 
local choiceFrame = script.Parent.Parent.Parent:WaitForChild("ChoiceFrame")
local message = choiceFrame:WaitForChild("ConfirmationMessage")  
local frame = script.Parent.Parent.Parent:WaitForChild("OptionFrame") 
local sound = script.Parent:WaitForChild("Splash") 
local fire = script.Parent.Parent:WaitForChild("FlameReaper") 
local water = script.Parent.Parent:WaitForChild("Aqua") 
local earth = script.Parent.Parent:WaitForChild("EarthGuardian")

button.MouseButton1Down:connect(function() 
	if frame.Visible == false then
		--Set frame to visible
		frame.Visible = true 

		--Show players the message
		message.Text = "Are you sure you want to choose "..name.Value..", a Water type Element as your starter Element? Answer with ('Yes' or 'No')" 
		
		--Hide the player's element Guis
		earth.Visible = false 
		water.Visible = false 
		fire.Visible = false 
	end 
end)

button.MouseEnter:connect(function() 
	wait(0.2) 
	sound:Play() 
	sound.Volume = 0.5 
	wait(1) 
end)

button.MouseLeave:connect(function() 
	wait(0.2) 
	sound.Volume = 0 
	sound:Play() 
	wait(1) 
end)