RE: Question about planted aquarium and fishless cycling
Zebra Danios are hardy fish. They are known to be able to live in polluted water for a while. Some people even use them to cycle the new aquariums and they can usually live for quite a while even there is ammonia in the water. So if they died so quickly, it is unlikely the low level of ammonia is the main cause while it can definitely contribute to the death.
Double check your readings on ammonia and nitrite. It is the best to keep ammonia at 0ppm. If there is indeed ammonia, do a 50% water change to lower it.
There are also other things to check on. For example, the water temperature. I'd keep it at 76~80F. Use a thermometer to take the reading instead of trusting the heater's setting.
Aggression can cause deaths. The fish with most of its fin gone should be the result of attacking. Stress sometimes can weaken fish's immune system and make them easily catching illness. Fast moving fish like Zebra Danio can stress out the slower fish like guppies.
When everything looks fine, including the readings, no overfeeding, and no aggression. Then the problem can be the weak fish. Some fish stores sell low quality fish raised on fish farms with low standards. Some fish farms even use a lot of antibiotics in the water to prevent the fish from dying in masses. Once these fish no longer receive antibiotics, they can die easily to diseases.
And finally, don't stress out over the losing of fish. Anyone who had kept fish for long enough must have experienced it. We were all beginners once, and many of us had to learn everything from trial and error etc. Even in perfect conditions, fish can die from time to time.