From the test results, you clearly do have a ammonia toxicity issue, but the source of that ammonia, I can't without more info (overfeeding, too high bioload, not fully cycled filter, something rottying, ammonia from chloramines, etc)
API Tap water conditioner does not detoxify ammonia.
http://www.oscarfish.com/water-conditioners/api-tap-water-conditioner.html
I still don't know if you have chloramines in your tap water, but if you do, API dechlorinator will just remove the chlorine from the chloramine, but not the ammonia that unbinds from the chloramine, which would result in ammonia levels which are toxic to fish.
If chloramines are the case, I would suggest switching to a dechlorinator that detoxifies ammonia, such as Seachem Prime or Amquel. (Prime being the better option)
If the nitrifying bacteria in your filter are well, they should be able to clear away the ammonia shortly
So again, if the ammonia is from chloramines, doing a water change won't help unless you get Prime. But if the ammonia is from another cause, water changes are recommend to bring the ammonia levels down. The source of the ammonia should be addressed appropriately.