How to save string values through data stores?

The problem here is line fifteen where you put child[i].Name. Child is a table containing the children of the Characters instance and does not contain numerical indices.

In order to fix this, iterate through the children using a generic for loop so that you can get the value directly from each pass of the loop. This would be implemented like so:

for i , v in pairs(child) do
	v.Value = ds:GetAsync(ply.userID..v.Name)
end

Because data stores are stored in the Roblox servers, they are prone to error due to problems like connectivity. For this reason, your call to GetAsync should be wrapped in a pcall() function to handle any possible error correctly. In addition, a player joining for the first time will have a nil value for the player's corresponding data store. You should check if the value from the data store exists or not before using it. If it doesn't, set the value to some sort of default. Your final listener function to the PlayerAdded event should be this:

game.Players.PlayerAdded:Connect(function(plyr)
	local a=Instance.new("StringValue")
	a.Parent=plyr
	a.Name="Characters"
	for i=1,#stats do
		local stat=Instance.new("StringValue")
		stat.Parent=a
		stat.Value = "None"
		stat.Name=stats[i]
	end

	for i , v in pairs(plyr.Characters:GetChildren()) do
		local success , value = pcall(function ()
			return ds:GetAsync(plyr.userId..v.Name)
		end)
		if success then
			if value then
				v.Value = value
			else
				--Player is joining for the first time
				--and datastore is empty
			end
		else
			--handle error here
		end
	end
end)