I wouldn't be concerned with Ph, GH and KH at this point. The elephant in the room is your nitrites. They are more lethal than ammonia and you need to continue large daily water changes until they go away. Like said, heavy doses of Prime (per the bottle) will detox the nitrites (or ammonia) for a portion of the day, but those daily BIG water changes will be the true life saver.
As probably said, one thing that would speed along a proper cycle for this tank would be some healthy, seeded filtration media.
Feeding extremely lightly and skipping days of feeding is very wise until your tank produces nothing but nitrates.