Charcoal has nothing to do with clamped fins or anything. It won't harm your fish. Charcoal/activated carbon only lasts for a few days anyway so at this point, unless you just put it in a few days ago, it's already expired. It typically only lasts about 3 days to about a week or maybe 2 weeks if your tank is very clean. So don't worry too much about that, it's not important or necessary. It will only remove meds if it's fresh/new.
Was his tank bare before like that? No plants or anything? If so, you definitely need to invest in plants of some kind. They don't have to be live, but any silk or fabric will do. I like the packs from PetCo if you've got one near you. Those will help out. Basically, Betta's are top dwelling species, their territories are at the top of the water primarily and if they have nothing to hide in, they can get stressed out pretty badly as you see in your fish here. Tall plants are ideal, small ones or hides aren't as effective. Of course, as you noticed, he will use the hides if that is all he has. I definitely recommend getting some sort of plant, ideally the tank should be filled with plants so he can swim in and out of them. That's the funny thing about fish and animals in general; the more hides and plants you give to them, the safer they feel which means he'll be out and about more often!
The second thing is that Betta's are tropical and they do need heat. Ideally somewhere between 76-82 is ideal. 78-80 is the target zone. So getting a small pre-set heater or getting a Hydor Theo 25 Watt (perfectly safe for a 1 gallon) from drsfosterandsmith.com is the best way to go. Don't get a heater in a store if possible, they're terribly overpriced. Even the addition of shipping, it's cheaper on drs foster and smith
You can however get a cheap glass thermometer from Wal-mart for about 2 bucks. This way you can at least know the temp of the tank.
Water will either stay cooler or warmer than the air temp depending on the size/body of water. Usually these small tanks, if they start off cooler they're going to stay cooler. So even though your place is around 70, this likely means that his tank is more like 66-68. That's much too cold. What happens is their metabolisms slow down and they don't eat as much, they can get stressed and sick. They can live longer in these conditions which is why you may hear of Betta's living 5 plus years in a non-heated bowl with no water changes. Yeah, they live longer but is the fish really living? Are you getting the full experience? I understand that some people don't understand why you'd want to "experience" a fish, but when they're active and happiest, they act just like water puppies.
So when you can, definitely look into a heater and a thermometer!
Sounds like you're feeding Hikari betta pellets. Not super terrible but not good either. If you have the resources to, I would upgrade to NorthFin Betta bites, they're only found online as they're a Canadian food that just made it's way into the US (exciting!!). It's the best out there, a smaller container than New Life Spectrum; the second best out there, and it's a bit cheaper than NLS IIRC which is good for you! Good nutrition is the next step after getting a heater ideally. Without it, the fish can lack some serious nutrition that is necessary to keep the fish healthy. Most of the "lesser" foods contain a lot of fillers that you have to watch out for; corn, soybean, and wheat. Wheat is used as a binding agent so it's not as bad but you definitely don't want to see the first two in the first few ingredients ideally.
So, you've never done a water change on him except for the week before be became ill, is that correct? Also, even if you leave out the water to gas-off, you should still condition it with your water conditioner. There might be something else in your water that is harmful. Also, if you're on city water then the chlorine isn't the problem any more, it's the choramine which sticks around much longer and doesn't gas off quick at all. So definitely use that conditioner. You can still set it out to let it match temperature though. That's a big thing, you don't want to shock him too much by doing too big of a change all at once or using different temperature water going in ideally. Some degree change is going to happen, but you don't want to have the water at 68 and then add in 50 degree water of course lol.
The gravel vacuum is a siphon hose that you can use to do water changes. This way you can leave your fish in the tank and suck out the nasty stuff in the gravel. A lot of uneaten food and waste gets trapped down there and if you don't clean that out, the ammonia stays in there and can harm your fish. The Dip out method is simply stirring up and poking at the gravel to get the nasty stuff up, then you use a cup to dip in and capture that waste and water in the cup and remove. Taking out as much water as you need for the change. That's all that means. So if you take your fish out and dump out the water and clean the gravel, you're doing neither of those things which is fine. It's just less stressful to leave him in there and use a gravel vacuum for a water change.
But overall, it seems to me like he's just stressed out. He needs more places to hide, some heat, and a few more small water changes so you don't shock him
I know it can be a lot to comprehend so please do ask questions if you've got them! All of this has a huge learning curve to it, so don't beat yourself up if something doesn't click right away! It takes time!
