For the .05 it would be about 7.8-8ppm and for the 0.02 it would be about 3 ppm (a little under .02 like .019)
That's right! Good job. Make sure you measure pH right. pH affects the equilibrium strongly!
As Rocksor exactly says. I am with him. You need nothing now but patience, testing, and time. The mentioned ammonia alert wouldn't hurt but help.
Ive been watching so many tutorials and the most effective way I've seen is to get established media.
Not necessarily. It may speed up the cycling , depending how much of the established media you introduce. You can take a whole established filter from one tank and install it on a new tank and the new tank would be cycled more or less, if the filter capacity is sufficient for the amount of fish in the new tank.
I have gotten device from thebiggerthebetter and once the free harmless ammonia levels reach .05 i will do a 20-50% water change and add some agent like prime.
Please read my and Rocksor's advice more carefully. It's either a WC or Prime. You could do both too but understand why you do it and what you want to accomplish, like get away with a smaller WC, or to create a margin of safety against future ammonia rise, when you cannot be home, etc. Beware that Prime interferes with the API testing and you will need to learn how, so you don't get confused. This is one reason I prefer Ammolock or even WC's as Rocksor said.
I hope this shows you that i understand the basics of the nitrogen cycle.
Nope. You've learned how to test for ammonia. That's all.
As before, I propose again you read a few articles on the net, on MFK, etc. on nitrogen cycle in a fish tank as one homework. Whatever you don't get - ask here.
As a second homework, find out what disinfectant your city uses on your tap water and how much - your parents should normally receive an annual water report from your municipal water authority or you can find it online on their website.
You also seem to need to work on how to feed all your fish evenly, as we discussed. Divider, or spot feeding, etc. if the problem of one fish hogging most feed continues.