I thought you said that you have a rock in your tank that was from a Petco tank (with the anemones). If you do, then that's an established live rock (since it was established with beneficial bacteria) in their system. Another would be great.
The ammonia spike is not unusual - you're going through a pretty standard cycle and you'll continue to read ammonia for a bit. You should also start getting nitrite soon. Fish and food create waste which creates ammonia and as long as you have fish and feed them, they'll continue to produce ammonia. Eventually, your bacteria will efficiently convert that ammonia to nitrite and then nitrate preventing a buildup of toxic ammonia. But because you have fish in there and ammonia is toxic to fish, you've got to take extra measures (hence the extra water changes, addition of Prime, etc) to keep ammonia from building up too much. If it weren't for the fish, you could just let it ride until you stop reading ammonia and start reading nitrate.
