Welcome to the world of fish keeping.
For starters, you have the filter situation slightly wrong. Clean is not necessarily better when it comes to fish. Fish come from a world that is slightly dirty and within that dirt are microbes that convert all your bad chemicals ( ammonia and nitrites) into non or less toxic chemicals like nitrates. Here's the thing tho, and I hope I don't confuse you, the toxicity of the ammonia will all depend on the pH of your water. In water with a pH below 6.8, toxic ammonia is converted naturally to non/less toxic Ammonium. That's a good thing. Here's the issue with your situation: while rare, if there is a lot of ammonia or ammonium, the API test can come out so green that it verges on blue. The problem is with the stock you mentioned, it's highly unlikely that they are producing that much ammonia in that sized tank in such a short amount of time unless it's also coming from uneaten food or it's coming from your water company. Unfortunately, posting pictures can be misleading because of how OUR screens are set up. If the color grades don't match the ones you used to post the pic(s), it's not necessarily going to show what is actually there. Since you say your are colorblind, I strongly recommend you switch from color coded tests to digital testers where the values will comes out in numbers and not colors. It will cost a little more for these types of test probes but for your situation, unless you can have someone local to you read your results, you really shouldn't trust what you see. Which brings me to this: Since you are getting very different results, I'd take a sample of your tank water and your tap water to a store and have them confirm what the result is. Don't let them give you a " It's good" or " The water's fine" type answers, get actual numbers/ values and here's the reason why: Below is a picture of the " cycling" process in graph form.
View attachment 392031 As you can see in the graph, ammonia will go up and then go down as will nitrites. So if you get a value of say, 5.0 ppm, unless you are testing regularly, you won't know if that 5.0 is on the way up or 5.0 on the way down and that's important to know because they will look the same in both directions but their meaning is very different.
Now for the kicker,
the microbes that are doing all this converting of ammonia to nitrites and nitrites into nitrates, do not live well in water with a pH below 7.2 So if you have ammonia( actually ammonium) in low pH water, that's more workable than if you have ammonia in higher pH water because ammonia is a killer.
So for now, before going crazy changing anything, get your water tested so we all are working with the same numbers.
As for the filters: The microbes that do all this converting, live mostly on the surfaces in the tank where there is the most oxygen in the tank and usually, that's in the filter which means the filter cartridges so it's okay for the cartridges to get dirty but all you need to do is rinse them off in water ( best is tank water you are going to toss from a water change) if they get clogged so that water flows through the cartridge. The carbon in those filters only lasts maybe a month so it's basically useless long term for filtering but it's a good source of surfaces for these microbes to live in.
So as you see, this is not like a wrench where an oily one can cause slippage on a bolt so you want a clean one to work with but rather a little dirt isn't going to mess things up and can be very helpful for keeping the water, the most important part of fish keeping, clean.
Hope this helps.
