Why is "player" of type "nil?"

Only LocalPlayer can be used with LocalScripts. However, MarketplaceService must be used with normal Scripts. Therefore you cannot use LocalPlayer; Instead you must parent up to the player itself.

Let's assume that the script is 4 down from Player. That means script.Parent.Parent.Parent.Parent would equal the player. I don't know the hierarchy of your GUI, so you must count the parents until you get to the player. Check out Line 8.

local MarketplaceService = game:GetService("MarketplaceService")
local ds = game:GetService("DataStoreService"):GetDataStore("countdowncreditservice")
local productID = 20518668

local buy = script.Parent

buy.MouseButton1Click:connect(function()
    game:GetService("MarketplaceService"):PromptProductPurchase(script.Parent.Parent.Parent.Parent, productID) --In explorer, let's say that your GUI looks like this |Player > PlayerGui > ScreenGui > BuyButton > Script| That means you need 4 Parents, since you go 4 up from the script, which equals the player. If you have a frame or something which holds the Buy Button, add a Parent.
end)

MarketplaceService.ProcessReceipt = function(receiptInfo) 
    for i, player in ipairs(game.Players:GetChildren()) do
        if player.userId == receiptInfo.PlayerId then
            if receiptInfo.ProductId == productID then
                player.statistics.credits.Value = player.statistics.credits.Value + 1
                local key = "plyr-"..player.userId
    local savedvalue = {player.statistics.credits.Value}
    ds:SetAsync(key, savedvalue)

    return Enum.ProductPurchaseDecision.PurchaseGranted 
            end
        end
    end
    end

You can read more on hierarchy here.

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