Textlabel getting moved each time a new one spawns?

Well, I see no attempt of you trying to push its position down. What you need to do is set a variable, that would contain the last TextLabel, or its position. So:

LastLabel = nil

game.Players.PlayerAdded:connect(function(player)
	local label = Instance.new("TextLabel",script.Parent.SurfaceGui.Frame)
	label.BorderSizePixel = 0
	label.BackgroundTransparency = 1
	label.Size = UDim2.new(1, 0, .05, 0)
	label.Font = "ArialBold"
	label.FontSize = "Size36"
	label.TextColor3 = BrickColor.White().Color
	label.TextStrokeTransparency = 0.5
	label.Text = player.Name.." - "..player.userId
	if LastLabel ~= nil then
		label.Position = LastLabel.Position + UDim2.new(0, 0, .05, 0)
	end
	LastLabel = label
end)

game.Players.PlayerRemoving:connect(function(player)
	if script.Parent.SurfaceGui.Frame:findFirstChild(player.Name.." - "..player.userId) then
		script.Parent.SurfaceGui.Frame['player.Name.." - "..player.userId']:Destroy()
	end
end)