Doesnt that then become 40ppm of nitrite and then 40ppm of nitrate?
No. It doesn't. You're thinking this waaaaay toooo much. As someone earlier said, cycling isn't rocket science. You can make it into that, but it doesn't need to be.
I'm going to try this one more time...
Your nitrites, in reality, ARE decreasing. But just as fast as the bacteria is converting the nitrites to nitrates, your other bacteria are converting the ammonia to nitrites. You are converting nitrites to nitrates, but because of the constant addition of ammonia, you're replenishing those nitrites as fast as you're eliminating them. The bacteria that convert nitrites to nitrates just haven't gotten over that population hump yet to start decreasing them. You say you're studying electrical engineering... read up on feedback loops and you'll get a sense of what's going on.
The amount of ammonia you've put in that tank is FAR more than folks normally put in during cycling. Way more. So don't expect your cycle to behave like everyone else's. It's going to take a while - assuming you stop putting stuff in your tank to create even more ammonia.
Yes... all salts claim to be phosphate free and nitrate free. They aren't. Granted, the amounts in there aren't much, and may not even be measurable depending on your test kits, but it's in there. For example, Reef Crystals has between 0.2-0.5ppm nitrates in it. All living things need phosphates to some extent, so in that respect it's just one of the hundreds of "essential elements" that is in your salt mix. Copper is a big no-no in reef tanks too... but you'll find minute amounts of copper in salt mixes because again... it's an essential element for life.
This isn't going to fix itself in a matter of days. Yes.. your nitrates are coming from your ammonia and nitrites. And you're going to continue to get more and more. And until you stop dumping junk in the tank, (including food), you'll just keep seeing the levels go higher and higher.