Sorry things aren't going the way you expected. As paulabob says, aging cheese with a natural rind is tricky. I consider it at least a tricky as making the cheese in the first place. What's worse is that available instructions about it are poor. I don't have time to write a whole big thing, but search around for some of my long posts on the subject for a bit of a beginner's guide.
To answer the questions:
1. You should never cut the rind. That rind is the protection for your cheese. I really don't recommend re-aging your cheese after you have trimmed bits off of it. Fresh cheese is delicious. Cut your loses and have delicious cheese now, rather than potentially not-delicious cheese later. In fact, I always recommend to people to plan to make 5 or 6 shorter aged cheeses to get the process down before they attempt a long aged cheese. You can count this as #1. It's all good.
2. Softening of the paste is a normal part of aging. For a hard cheese, obviously you don't want it to be that soft. Very many things could have gone wrong -- all the way from the beginning of the make into the aging. One of the reasons natural rind aging is tricky is because you have to get a lot of things right in a row. When you first start, it's easy to get a few things wrong. If you age it long enough, it will probably go bad when you first start out. That's why it's best to start with shorter aged cheeses and bail as soon as it seems to be going sideways.
3. Eat it :-) It will be delicious!
4. Humidity is probably the most important thing about aging cheese. What humidity you want depends on what you are trying to accomplish. In general, though, the cake carrier is probably a good thing and the moist paper towel was not. More later.
5. Make more cheese! I know you are bummed and maybe you need to take a break. However, you *will* get beyond this! Even though I say aging cheese is tricky, once you get the feel for it, it's very intuitive. For a lot of experienced makers, it almost seems fool proof. They forget the difficulties at the beginning and often give poor advice. Don't worry!
Very quick general advice: Mold and yeast grows on cheese. When you are doing a natural rind, you *want* mold and yeast growing on your cheese. However, you need to select what it is that should be growing. When you see videos and recipes showing you how to avoid mold and yeast on your rinds, you are seeing videos and recipes from people who are inexperienced with aging natural rind cheeses. Often they have disasters that they may or may not talk about.
When you first make the cheese, there is about a 1 week period when things generally won't grow visibly on the rind. After that, things start to grow. If you cover the rind with honey, oil or other things before things grow, you will normally have big problems. The yeasts tend to burrow into your rind and produce structures that will cause your rind to be in very bad shape. You should normally only coat your rinds after the initial growth period is over (at about 4 weeks time). Even then, it's a technique I don't recommend to beginners. The first 4 weeks are the most difficult for aging cheese and when you get to about 8 weeks there is barely anything to do. You aren't making it *any* easier for yourself with these techniques. They are there for other reasons.
You should learn how to age your cheeses out to 4-8 weeks before you start thinking about longer aged cheeses IMHO. It reduces the learning curve by a lot because you aren't waiting 6 months to see how your cheese turned out. Once you can do the first 8 weeks easily, everything else will fall into place. You may consider doing a couple of bloomy rinds first. The white molds on those cheeses are beasts and they are the easiest things to age.
After that, try to make something like a tomme and age it out to 4-5 weeks. The main technique is to make sure the cheese is not wet. It should never be shiny. Dry it off it is is. Flip your cheese *every day* and inspect it. Mold that you don't want shows up before you know it.. I flip my cheeses every day even after 5-6 months. It takes seconds when things are fine. It saves your cheese when they aren't fine.
Always wipe all surfaces on your cake carrier down every day so that they are completely dry. If you have the humidity right, it should fog up over the day and you will be able to dry it easily. The cheese will not be wet. If it's too dry, lower the temp a bit. If it's too wet, raise it a bit. That's the easy way. Otherwise don't worry. If you can't get it moist enough, then possibly you need a smaller container. If it's always too wet, then you need a bigger container. It will always be wetter at the beginning.
Your cheese will grow stuff. If it's white, leave it alone. If it's blue, then brush it off with a very soft brush or cloth. If it's black, grey, brown, then your humidity is too high. Don't panic if it stains the rind. It's fine, but you will need to reduce the humidity. If it's orange or pink you need to reduce the humidity ASAP. It's still fine, though.
Your cheese will smell terrible. Often like mushrooms and/or farty broccoli. That's normal for a natural rind. If it starts to smell like gym socks, then reduce the humidity ASAP. It's still fine, though.
If you can't control the blue, then give it a wash with a 3% brine solution *once*. If it goes uncontrollably blue again, then you should probably just wash it off again and eat it. Next time keep the temperature a little higher and the humidity a bit lower. If it goes uncontrollably red/pink/orange and smells like sweat socks, then you have made a washed rind cheese. Eat it up quickly. Next time keep the humidity *much* lower. If the rind cracks, then the humidity was too low. Eat the cheese and use a smaller box with a slightly lower temperature.
At some point you'll have a cheese covered completely in white/grey mold and it will start growing different mold. This will happen somewhere between 4-6 weeks out usually. That's the "succession mold". At this point you have a lot of options including doing nothing and just continuing at you have been doing. But this is the "winning condition" for aging cheeses.
There is much, much more to this, but these are the basics. There will be advanced people doing things differently than I've mentioned here. That's cool. It's much, much more complicated than I have said. This is just to get you started.
Or you can vacuum pack or wax your cheeses. That's boring, though :-)
Edit: And yes. This is *not* my "whole big thing" post on the subject...
