Poor baby. :(
My first impression of this fish is that he looks cold, you said you try to keep the temperature between 72-80 degrees, but the range should really be consistently 78-83 degrees. This may sound kind of silly to warm-blooded animals like us, but cold blooded animals depend on temperature for their entire metabolism. Cold fish are often pale and inactive, the also have digestive problems because when the temperature creeps lower, it slows down the whole digestive process. This causes food to stop in the gut, and the fish to bloat. This puts pressure on the swim bladder, so the fish can no longer control its depth in the water. I think if he is at a consistently warm temperature, he will be like a whole different fish.
He also seems like he could be nibbling on his fins--fin rot looks totally different from that. Fin rot is the result of a bacterial infection typically caused by ammonia burns--this infection looks like a black crusty band on the edge of the fin. Because of how rugged the edge is and the face that it's still clear--I think that he is nipping it. This could be a result of the temperature fluctuations occurring in the tank as well as the fact that the tank is small and doesn't have anything for him to hide in near the top of the water. Stress and boredom are common triggers for tail biting, though it is very very rare that you ever see them do it.
Dip testing strips are very overpriced--they are also very inaccurate. The liquid drop testing kits are a bit more expensive than the strips, but they are much more accurate and you get hundreds of tests out of them rather than a mere dozen. You can also bring your water to any fish store and have them test it for you for free.
Spring water is also not a good idea--dechlorinating products may look pricy in the store, but spring water costs really add up when you're changing the water as often as you have to in a tank that small. I highly suggest switching to tap water and dechlorinator--it is not only more cost-effective, but spring water does not contain vital minerals that tap water does. These minerals buffer pH and helps the water parameters remain stable.
Also, you should consider that generally the water changing schedule should be 100% every other day for a 1G tank. It's possible that due to the infrequency of 100% changes, some ammonia is building up in the tank. This may be the reason for some of the tail biting and the clamping of the dorsal fin. After all, if you do one 50% change, and then another 50% change right after it, there's still some of the original water left over, plus the ammonia that the fish produces in between changes. You also should consider forgoing the use of aquarium salt and melafix and just seeing what good clean water can do for you. As long as the water is clean, the fins will not get infected and will heal on their own. Extra salt and other chemicals in the water stain the fish's vital organs--I would avoid using them for extended periods of time. I only use salt a for a few days after I notice fin damage or a wound--it's not something you use all the time.
So to sum up, really, I'll give you some shopping ideas. The first of which is to never shop at a pet store. Retail stores have a lot of overhead, so they have to jack up the prices so that they can make a profit. If you shop online, you get a much better deal. I use http://www.fosterandsmithaquatics.com
for everything--you will find that all of their items are at least $10-$20 lower than what you get in pet stores, and everything ships for a very reasonable $9 flat rate. So even if you get one item, you still save a dollar usually, even with shipping.
In my opinion, you should seriously consider getting these items:
This 25watt heater will keep the temperature consistant and warm enough for your fish to be comfortable. Smaller heaters are low quality and don't keep the temperature stable.
This is the best dechlorinating product you can get for the money. It is concentrated, so even though it's a tad more expensive, you still get more doses out of it that you would other similar products.
For the price of a dozen inaccurate strips, get hundreds of tests out of this liquid test kit.
Pick out a nice bushy silk plant. You might want to get a couple so you can swap them out from time to time. This gives the fish more security, since they have to go to the surface to breathe, they need some cover over that area, too. Believe it or not, fish also get bored. Swapping out different plants helps stimulate them.
I also think you should get your fish a larger container. Generally, heaters like the one I linked to are safe as long as you can submerge them up to the water line, but they are designed for containers that are two gallons or larger. I understand that you are strapped for cash--so a good alternative would be to get a rubbermaid or sterilite plastic storage bin at walmart or target. They're not very pretty, but they make wonderful habitats for fish since they are long and shallow, and they are extremely cheap. A 2-4 gallon container is only about $3. Very reasonable. Keep in mind that larger containers also do not need to be cleaned as often, and plastic storage bins are much more light and durable than glass bowls. Anyway, it's a good idea to have one around until you can upgrade to a better tank.
Good luck with your fish, I hope he starts turning around for you. By the way, I think it's nice that you're doing the best you can for the little guy. :) Things will get better.