Agree on API giving false readings and its the other way around, They often read lower than shown. For cycling. the typical process and green light is adding your bacteria and then ammonia chloride. Then you want to monitor ammonia and when your ammonia is steady at zero for 5 days and Nitrate is steady at 20 or below- You are cycled. Ignore nitrIte Unless sky high
The tank will go through two phases in which ammonia will rise then fall and nitrate will rise and fall which is normal. When fish are added, the bacteria population will increase with the new bio load, converting waste to nitrate.
As for adding a fish, to confirm your test results, take a water sample to a store that does NOT use Api kits and have them test your ammonia and nitrates and compare readings- then you'll know where your levels truly are at