with nitrates being at zero, your tank is not cycled at all right now. daily water changes with Prime dechlorinator are a must to keep those ammonia and nitrite numbers at zero.

just to confirm, your test kit is a liquid drop kit, preferrably the API kit? dip strip tests are horridly inaccurate.

your nippy goldie may be hitting maturity, and showing dominance to the others. keep an eye on him, and be ready to rehome him if necessary. i personally would rehome all of the goldies and get fish more suited to that size tank.

ah, just saw the photo. the aggression is most likely due to the tank being too small, the fish not being able to establish their own territories in such a small space, and there are no hiding spots for them to retreat to at all. add more plants, some wood or rocks, etc to create spaces each can call their own.

are the edges of your tank hanging off whatever it is sitting on? very dangerous. all parts of the bottom trim of the tank need to be supported, or else the glass and/or seals can be stressed, and you could have a disaster on your hands.