Sounds like he is dying. Not much you probably can do at this point though. If his fins are rotting, that is called "fin rot", and is a secondary symptom of the water not being very clean.

However, Betas are not long lived fish anyway. My only recommendations would be to add a little salt and maybe slowly raise the temperature to 82-84degrees F. At 82-ish, tropical fish's immune systems kick into overdrive. What is "room temperature" for you? Betas really are tropical fish, and prefer warmer temps than what most people's homes are in the winter. And add some table salt, about 1 teaspoon per gallon. That will help him develop his slime coating on his scales.

I don't think changing his surrounding/decorations will help. He's probably not bored. Betas don't really like to do much but sit there.

Agree with ric. Room temperature is about 65F unless you have the heat kicking, way to cold for a tropical fish. The light may add some heat but makes it fluctuate even more. A 1 gallon tank with the maintainance schedule you mentioned is not adequate. Small tanks are really more for an "advanced" hobbyist. Change 10% of his water daily, but for know I would change 50% today and 50% tomorrow. Remove any uneaten food and fish poop. He will also eat regularly when the heat is between 76-80F. Low water temps will slow his metabolism and make him lathargic. Just improving the water conditions will help, but must be done soon if its not too late allready. I know bettas are marketed as being kept in bowls with no heat, its just a bunch of crap. As far as not being a long lived fish, I think thats more because of the conditions most are kept in. I have had some live 5,6 and 7+ years. As far as "betta depression" , although it is not out of the question, it is used way to frequently as an excuse for health issues from not having proper parameters. Don't take this the wrong way hope, like I said they are marketed by fish stores this way, and it is confusing when a fish store person gives bad advise, most don't know their (!) from their elbow.

I can only add one thing to the above, they are one of the most active and amazing fish when kept in larger, heated and filtered (as you would any other fish but milder water/air flows due to long finnage) and planted tank. Think Asian. Like a puppy dog! They come alive with a wonderful personality.

Before mine got sick (as you can see from my posts so learning here myself) he was in a 20 gallon, and would swim all around, chase the other fish and poke at the apple snail.. He would sleep snuggled in a large curled plant leaf, in the area I made a plant bed for him, (in a curve of driftwood that was part in water part out)(little u shaped) then come out at day break. He would swim with the cory catfish up and down with them..

In my opinion, unless one is a breeder and space constrained they should never be in anything 'less' then you would place any other fish. ie the best environment to their natural one that we can provide for them. I looked at photos of their natural environment and nothing like a little bowl with nothing to do, lol. (I realize any tank is nothing like nature, but at least we can try to selectively come as close as possible)... I am hoping to learn more and buy from a breeder and give them the best care... They are worth the effort, I'll say...

So from my own experience, larger tank with heater and filter. Fin rot as woeisme said, and may be to late, but Maracyne two seems less harsh then others I tried. (one of mine died, as one thing cleared, something secondary showed up, then finally fin rot, and he just was too tired from weeks of treatment and the stress of it all) both from local store in those horrific dirty little cold bowls.

Best to you... Sherry