Cycling a tank refers to a process that all new tanks/filters go through. The basics of what happens is ammonia builds up in the tank from the fishs' waste; this is very toxic to your fish. Some good bacteria build up and turn this ammonia to nitrIte. Once again, while this is a LITTLE less toxic, it is still highly toxic. Another set of bacteria will develop which turn the nitrIte into nitrAte. NitrAte is for the most part non-toxic, unless in really high quantitites. Eventually, when you do the water changes, all you will be doing is removing some of the nitrate from your water.
What was the amonia conditioner thing you used? Right now, it is probably best to return maybe 6 of your fish, and wait for your ammonia and nitrite to return to zero (about 6 weeks) before adding more fish. This will help keep your fish healthy and be alot less stressful for you. However, you probably will need to be doing daily water changes to control the ammonia in the tank.
pH- In general, you don't want to mess with the pH in your tank. Using chemicals to alter your pH will cause it to have swings, which are alot worse for the fish. This can also lead to other problems. Your fish will adapt to your pH. Just make sure you add a little tap water to their bags until their pH is close to the pH in your tank.
Dechlorinator- on the list of things you used in your tank, no where on that list was a dechlorinator. This is something you do need to be using with every water change. Chlorine and chloramine is very deadly to fish. Most dechlorinators will also remove heavy metals, which are also bad for fish.
Ok, i think that about covered everything you didn't ask about. As for the fin nipping, I have 4 zebra danios (used to be five), and I never saw this. It might just be a teritory thing, and also the stress of the move, exploring their new environment, etc. Just be sure to keep an eye on it.