Good job hillmar! You're only 3 days in to your qualifying week so try to hold off at least until Sat/Sun if you were thinking of adding the first cory this weekend (just to further verify you're not going to get a mini-spike.
I personally agree with the cory addition plan (some might give you a hard time) and I think one at a time with a week is prudent since your biofilter is still extremely young. After the tank is a year old or so your filter system will be fully mature and 2 or 3 of that size would be ok for a single introduction (if you were for some reason stocking, that is.)
The weekly water change is one of the great principles of successful freshwater keeping for beginners. Its not about just the 3 numbers you've been looking at, its more. There are actually hundreds of substances (heavy metal ions, large organic molecules, all sorts of stuff) in a running aquarium ecosystem. We can't afford and wouldn't have the time to test for all of these things but we don't want them or the overall mineral content to build up over time. When water evaporates (as its doing from your aquarium daily) it leaves behind all the mineral salts that came in with the tap water or other things. If you were to just keep adding water, the mineral content would get higher and higher.
The fish have very well-developed systems for separating the mineral content of their cells from the mineral content on their surrounding water, but those systems can only operate effectively within a narrow range. If the water slowly got higher mineral content, the fish's system would slowly track up with it and it would get used to it, but then when you finally performed a water change, the fresh tap water would be much, much lower in mineral content and the fish's mineral balancing system would be overwhelmed and the fish might die.
This is why the regular gravel-clean-water-siphon-out mainenance procedure is so important. The habit we want is for it to be weekly. We all will have weekends when we go on trips and can't do it and that's ok but the overall habit should be the weekly one. Deciding on the actual percentage to change can be somewhat complicated, but often the act of doing a good gravel cleaning will take at least 25 or 30% of the water out and that can be a good determining factor. Holding a steady nitrate(NO3) "trend" (comparison of NO3 readings over many weeks) is the real test. If you found your NO3 was creeping up, you would definately want your water change percentages to be higher.
The weekly water change is also the time when you do other maintenance items get done. You wipe down your inner walls for algae (even if you don't see it) and clean other things (never using soaps or anything like that of course, soaps hurt fish.) Each week I rotate to a different "extra" thing to focus on, like a good cleaning of the tank top or the upper rim or something that needs it.
Filter cleaning and maintenance is a whole 'nother topic
... Don't do anything to your filters right away hillmar, they still need to have a little more time un-disturbed. Just like the weekly water change, there should be a solid and regular habit extablished for filter maintenance and here in the beginner section we recommend that be first set to one month (or two weeks if that feels too long,) with the understanding that any time you observe reduced flow, you should investigate and potentially clean.
Most filter media never gets replaced, or rarely. Ceramic media like rings can last a lifetime and are just swished out in tank water during the maintenance. Sponges are gently squeezed in old tank water just to get the bulk of the debris out but not to disturb the bacterial colonies too much (the colonies are sometimes visible as a brown stain on the media.) If you have polyfloss or floss pads, those are the exception and do get replaced more often if they have broken down, but often they can go for months before that happens and can be gently squeezed out like sponges.
Eventually, some months from now, you will want to get two mesh bags and some new ceramic rings and start the process you mention of swapping out rings for the carbon. At each succeeding maintenance you take a little bit more carbon out of the carbon bag and add a few more rings to the second ring bag until its all switched over (acually, the 10G is so small, this can be done in two or 3 switchouts.) The Aquaclear will make this stuff easy. The Topfin will be harder since the bacteria will be on those spongy mesh bags I think. I believe when it comes time you will want to cut up that bag material with scissors and stuff the pieces back inside the new replacement filter media unit. This would be out at a year or two I think or whenever the material shows signs of breaking down. Most of the time you will just squeeze it out or swish it in tank water, just like normal sponges. There's more but this hits a lot of the first basics you need to hear.
~~waterdrop~~