Doesn't matter what stage of fishless cycling you are currently at. What you do with ammonia is always the same. You just carefully test such that your added ammonia brings you up to what you judge to be about 5ppm (basically guessing a shade darker than 4ppm on the API test) and then wait and measure 12 and 24 hours later to see what's happened. If your ammonia oxidizing bacteria (A-Bacs) drop the ammonia all the way down to zero anytime within the 24 hours, you don't recharge to 5ppm right away necessarily, but at whatever the "24-hour mark" was that you established with your first 5ppm addition. Usually people establish their 24-hour mark as morning or evening. You only ever add once in a 24-hour period.
Having ammonia in your tap water always worries beginners but its not a big problem. Once your filter is cycled, your bacteria will immediately eat all that ammonia just as if it were produced by other means! The only difference in behaviour for you will be to adjust your maintenance water changes (this is after you have fish, not during fishless cycling) so that they are a notch or so smaller percentages and more frequent (so for example if after you have fish, someone recommended that you do one 50% water change at a weekend, you might translate that into 2 25% changes, one during the week, thus diluting that ammonia even more, for less exposure to the fish.
As far as tap water ammonia supplying the food for a fishless cycle, yes, the ammonia will eat it and not know the difference, its just that it doesn't supply near enough and the cycle would take forever. In your case the fish food will have hopefully raised ammonia in addition to the tap water amount and you'll have made the current progress that way. It would be perfect if you could go out and easily buy a small pint bottle of ammonia as you are probably not that far from the finish, but usually its more like a half-gallon jug (in my case that was less than a buck though.)
~~waterdrop~~