How should I interpret these water parameters?

Yes, like the others said, you lost the cycle.  It was probobly throughing out the old filter that did it, not the water change.  Large water changes can stress out fish, can change the temperature and other water chemistry too much for fish.  But It should not have killed the cycle.  

You need to follow instructions for a fish in cycle. You will need to do more water changes.

https://www.fishlore.com/NitrogenCycle.htm

If you still have the old filter, run both filters together for 3-6 weeks.

An 80% water change has effectively de-cycled the tank and you will need to cycle it again-Never take out more than 1/3 of the water in a tank cleaning. Filters should be rinsed and reused until they either fall apart or there is a serious infestation in a tank. 

A 'Little bit' of ammonia is Never a good thing, monitor the water while you are cycling. And when taking a water sample, take the sample from the Bottom of the tank, don't just scoop off some from the top. 

Danios are a schooling fish, and there should be a minimum of 6-8, so that would be the next fish to add. 

But your tank is quite small. Might be a better idea to start a larger, like a 30+ gallon tank, depending on whatever else you want to add to it. Keep in mind that Danio's swim-constantly. So they need the room to move about. 

A little bit of ammonia is NOT okay. If you have ammonia the tank is not cycled. You need to look up Cycling a Tank With Fish. I think with proper care this tank will cycle fast, since it's been set up a long time. Stop doing water changes, just keep doing those tests daily. You want to see nitrite start to rise. This shows that the tank is cycling and the proper beneficial bacteria is growing. Keep up doing the tests. When your nitrite and your ammonia both drop to zero after 24 hours, the tank is cycled.

Buy a bigger fish tank. My gf brought over a 20 gallon fish tank and put four adult Crappie's in it. Disaster!