I prefer not to use carbon unless it's necessary for two main reasons. One, there is some research I have read that indicates long term use of carbon might actually be bad for fish, though it was certainly used for years because it kept the water clearer, and it is still useful for removing colour and odours if they exist.
Manufacturers have not caught up with this, and continue to put carbon in many filter inserts, leaving you no choice about whether to use it if you use the inserts, which is why I never use them. I put my own media in filters, even tiny ones can be fitted with some amount of bio media, like sponge, or even floss.
Much has changed over the past decades, as the latest poster has said. Carbon is useful for removing medication, bad odours and colour, like tannins, though the tannins are only bothersome to us, not the fish. Second reason I don't use it is that it isn't very good at growing bacteria, so I think you are better off in the long run replacing it with more bio media that can grow bacteria, which will assist in the nitrogen cycle.
Carbon can always be added if needed, then removed again.
As for the question about a test never showing ammonia, I would suspect a defective or expired test, or possibly contaminated reference solutions in the test, because fish waste is primarily ammonia. So it's there, in some amount, as soon as you add fish, or even snails. But a week or two, or even four, is nowhere near long enough for a filter to grow bacterial colonies unless it's been seeded with mature media to speed things up, so there must be ammonia, certainly after adding so many fish to a new tank.
If the test IS accurate, then the tank is not cycled, the fish are living in a low level ammonia soup all the time and though some fish are actually are able to adapt to such conditions, in some cases I have seen, the sad reality is that such exposure to ammonia always leads to shortened lifespans and greater susceptibility to opportunistic infections. Fish are like anything animal, they have a survival instinct and won't always show symptoms until they feel really terrible, because they know instinctively that looking sick means being preyed upon.
It can take several weeks to obtain enough bacterial growth to cycle a tank. It takes patience. Actually you are cycling the filter, really, not the tank itself. But tanks do grow biofilm, which is something many fish seem to need to do well. It is the reason you are told not to add certain fish species to new tanks.. the lack of biofilm seems to make a big difference, even if they do not actually consume it as food. Most shrimp don't do well at all without biofilm, and it grows at its own pace. You can't hurry it up. Trying to hasten filter cycling is best done with seed media from a mature filter, not by adding more fish.
When reading tests, always do it under the best light available. Daylight is best, light from 65 or 6700 K bulbs is next best. Always read them under the same light, so that you see the same colours each time. Different light makes colours look different, and many people have some trouble matching the test solution result to the colour charts, but good light helps a bit.
Also, take the test water from deep in the tank, rather than the surface, which might, possibly, be a bit more diluted than deeper water. I don't know if that last is actually true, but it cannot hurt to take samples from deeper down. I have a friend who swears the results are different doing it this way. I have not noticed much if any difference, but I keep different fish and use different filters so perhaps it is condition of his tank.
What brand is the test, and does it have an expiry date on it ? They do go bad over time, and then must be replaced. Do you have a test for nitrite & nitrate ? If you don't you need those too, you can't tell how a cycle is progressing without them.
Btw, once those swords grow they are going to be too big for that tank with those other fish in there. They can get to four inches or more. Old rule of thumb is one inch of fish body length, [not fins] per gallon of water in a tank. You have to factor in the adult size of the fish. And you have to deduct some volume for the substrate and decor that takes up space as well. Some say you can leave bottom feeders out of the equation, I don't think you should, especially if they are catfish or plecs, which contribute plenty of waste to any tank they're in.
