How come the value wont get changed and I wont get warned because of it?

Made a new variable since in line 36, it specified "PlayerCountries" and in the last code (your code), it was specified the cloned instance to be the parent of "PlayerCountrys" at line 30 (Just fixing a bit of spelling in mine)

I see no errors other than that. It should work just fine even in your script; it just means the script couldn't find the instance and then skips that line of code, then the next executes.

local Player = game.Players.LocalPlayer
local ReplicatedStorage = game:GetService("ReplicatedStorage")
local workSpace = game:GetService("Workspace")

local Buttons = script.Parent.Parent.MainGui.Buttons

local ValuesFolder = script.Parent.Parent.ValuesFolder
local PlayerCountries = ReplicatedStorage.PlayerCountries

if Player.Character then
	if PlayerCountries:FindFirstChild(Player.Name.."Country") then
		local PlayerCountry = PlayerCountries:FindFirstChild(Player.Name.."Country")
		if ValuesFolder.Country.Value == "" then
			ValuesFolder.Country.Value = PlayerCountry.Value
			if PlayerCountry.Value == "" then
				warn("Did not work as intended")
			end
		end
	elseif not PlayerCountries:FindFirstChild(Player.Name.."Country") then -- Dunno if you need this one, you can delete this elseif statements if you'd like.
		local PlayerCountry = ValuesFolder.Country:Clone()
		PlayerCountry.Name = Player.Name.."Country"
		PlayerCountry.Parent = PlayerCountries
	end
elseif Player.Character == nil then
	if PlayerCountries:FindFirstChild(Player.Name.."Country") then
		local PlayerCountry = PlayerCountries:FindFirstChild(Player.Name.."Country")
		if ValuesFolder.Country.Value == "" then
			ValuesFolder.Country.Value = PlayerCountry.Value
			if PlayerCountry.Value == "" then
				warn("Did not work as intended")
			end
		end
	elseif not PlayerCountries:FindFirstChild(Player.Name.."Country") then
		local PlayerCountry = ValuesFolder.Country:Clone()
		PlayerCountry.Name = Player.Name.."Country"
		PlayerCountry.Parent = PlayerCountries
	end
end

But if you're trying to execute the script after the instance has been added, then you can wrap it up in a function and then call the function. Or you can wrap it up using coroutine.

DevHub: coroutine

DevForum: What is Coroutine? by Mysterious_Myth11

DevForum: Coroutines - When and how to use them by ReturnedTrue

Youtube: Advanced Roblox Scripting Tutorial #33 - Coroutine by TheDevKing

Bit of advice: you can use "not" in an if statement

local bool = false
local nonExistent = nil
local Frame = script.Parent

if not bool then
	print("false") -- Will print
else
	print("this wont print because bool is false") -- Won't print
end


if nonExistent then
	print("This won't print because it is nil")
else
	print("This will print because it is nil")
end

Frame.Visible = not Frame.Visible
-- This turns the frame visibility boolean to the opposite boolean, e.g: true to false, false to true