Alright, my tank is developing into a mess of a cycle. Magically, fishes are alive and happy, probably thanks to chemicals. Here is a summary of what's going on:
Water got cloudy the second day I had the tank, and remained cloudy for 4 days, and turned crystal clear. Tests indicates that the cycle has not completed since I detect no nitrite and plenty of ammonia. Added Amquel+ to neutralize ammonia.
Two weeks later, water turned cloudy again, and has been cloudy for 4 days, with no signs of improving. Ammonia is going off the chart, but most of them is probably NH3 because the fishes sure don't look like they're poisoned. Nitrite is between 0.25-0.5 and has been that way since the water has been cloudy. Nitrate is 20, and seems to be slowly increasing. I tested my tap water and there is no nitrate so all the nitrates come from the tank.
So what is going on? I'm so confused...

Your tank is still going through its natural process of cycling. I wouldnt ad any chemicals to the tank while cycleing to nuetrolize the ammonia, i would stick with simple water changes each day if the params are too high. Is the ammonia beginning to go down? It should go down soon, and the nitrites spike, and then fall and then only be left with nitrates, but to me, sounds like the tank is cycling still. Just try to ease up on any chems.

It takes time, just be patient.

Amquel+ is great for neutralizing ammonia because it still makes the ammonia available to the necessary bacteria to colonize your system.

However, Amquel+ also binds and reduces nitrites and nitrates. So they may be in your system but are being locked up and not reading on your test kit.

Also, if your ammonia test uses brown color indicators (non-salicylate)you could be getting false readings of ammonia levels. If your ammonia test uses a yellow/green color scale (salicylate based test) you are getting correct readings.

So really it is a double-edged sword. On one hand you are neutralizing your ammonia but on the other you may not be able to track your cycle correctly.

Kevin