Hi aquababy,
I'm very sorry about your fish losses, I empathise as I've lost a number of fish in the past (a female guppy only recently due to dropsy), it's never easy but you did right by asking for advice on this forum. I've started keeping fish again after a gap of a few years. In terms of your bronze catfish, I know what it's like to have a fish jump out, just the other day I had to plop a zebra danio back in the water after it fell onto the carpet. And I love bronze catfish too, they're my favourite fish (I have six of them). I saw the pics of Stubby, he was a beautiful little fish and I can see why you got so attached to him, you did your best for him. Just try and think of the good times you enjoyed with him.
As you're kind of a beginner, it's very important you get sound advice and much of the advice given by others here has been good, but in my opinion not all of it. Firstly, there's the issue of water changes during medication. Basically, it's usually a bad idea to change water while you're medicating as the whole point of adding the stuff daily (or however often) it is to gradually build up the level of the medication safely, to kill the target organism(s). If you do water changes during a treatment cycle, you're just removing some of the medication before it's had a chance to work and build up to the required concentration in the water. That's potentially quite risky as it could lead to the pathogens/organisms building up resistance to the medication, which is not good as they won't be as effective in the future. Plus, the concentration of the med just won't be high enough to cure your fish; that's why they state the dose clearly on the bottle. You should generally do a water change before you medicate, and then after the treatment cycle is over, but not during (under normal circumstances). The only reason for doing a water change during medication is if you decide to stop using it for some reason, eg. if it's the wrong one and you want to change it, or if your biological filter is affected. If you're using the right med and want to treat with it full course and you do water changes at the same time, you'd have to add more medication to get it back to the right strength, which is a headache to work out.
Something else that needs rectifying is the idea that water changes are done partly to replenish oxygen in the aquarium somehow. No offense to the person who wrote it, but it's simply not true. The reason for water changes is twofold; to remove nitrates which accumulate from the nitrogen cycle, and to facilitate the removal of dead/decaying organic matter which lightens the biological load on the beneficial filter bacteria population. I can assure you that the water in any aquarium is constantly being re-oxygenated, otherwise no fish could survive in there. There's a chemical equilibrium between the gaseous CO2 and oxygen in the air, and that dissolved in the water (aqueous). It just so happens that oxygen doesn't dissolve very well in water, and CO2 does it better as it's a more polar molecule than oxygen. Temperature affects the amount of oxygen water can hold; the higher the temperature, the lower the dissolved oxygen (DO) level. Oxygen enters the water through gaseous exchange with the atmosphere at the water surface, and also through photosynthesis of aquatic plants (during light hours). The best ways of getting oxygen into the aquarium (or making more available) are to have plenty of aquatic plants, to have adequate surface turbulence from the filter and maybe an airstone or two, and to stock the tank lightly with fish. Of course, at night in the absence of light, the plants will respire like we do and make CO2 and use oxygen, which is why it's more important to run your airpump/airstone at night than in the day if you have a planted tank.
The other thing is the fish you have. As someone's already rightly said, minnows tend to like cooler water, so I'd recommend turning down the heater as suggested. Fish like neon tetras (again someone mentioned this) should only ever be added to a tank that's been running for some months, and that goes doubly for rummy-nose tetras, contrary to popular belief I don't think neons are necessarily a good beginner's fish, and rummy-noses certainly aren't; they're rather sensitive to water changes and need soft, acidic, mature water. If you want easy tetras, I suggest any (one) of the following: glowlights, x-rays, flames, black neons, serpaes, beacons. And it's important that whatever tetras you get, there's a group of at least five or six of that species as they tend to get stressed and ill if only kept in twos or threes; they're shoaling fish. For a small tank like yours, one shoal of small tetras would be at capacity, you can't really keep any other fish with them without overcrowding, and for a beginner, it's best to understock. I'm afraid others are right when they say your tank is probably too small for corydoras, they do grow to a fair size; bronzes get to 8cm. But don't worry, you can keep some corydoras if you want to (instead of the tetras), just go for a small species like pygmys, again, a small shoal of pygmy corys would be great in your tank (with no other fish). It's really just a case of deciding what fish you like the most and keeping within stocking limits for your tank; it's not easy to resist overstocking/choosing unsuitable species, but we all have to do it. Later on when you're more experienced and/or have a bigger tank, you can keep more fish, and slightly more challenging species. That's the thing about fishkeeping, it's kind of a long, enjoyable (but often stressful) journey, and when you start out, it's best to take it easy and slowly and get a feel for it. There are people who start out with difficult species like discus or rays, and some of them succeed which is great, but you save yourself a lot of heartache and disappointment if you build up slowly.
Getting back to water changes, again it's been said already but changing water every day or every other day is way too much. If your tank is cycled (0 ammonia, 0 nitrite) and stocked correctly, you should only need to do a water change every week or two. The point is that because you're overstocked you might have to do more frequent water changes, but the solution to that is simple: return some of the fish to your LFS until you're down to a good level (ask for advice on how to if you need it). Ultimately your fish won't do well in an overstocked tank, and even experienced fishkeepers find it challenging sometimes to maintain an overstocked aquarium in tip-top condition. It's just that an aquarium is biologically a finely balanced system even when not overstocked, and by overstocking you increase the risk of disease and water quality problems, and make it more difficult for yourself and your fish. Oh and you definitely need to get rid of the old tank water and replace it with fresh dechlorinated water when doing a partial water change, not just because it contains decaying organic matter, but because it also contains dissolved nitrates from the nitrogen cycle, which gradually build up in the aquarium and eventually become harmful to fish.
Also very important is fish compatibility, as you found with your betta, which is often a very aggressive fish (they don't call them Siamese Fighters for nothing!) I would suggest taking a bit of time to read some books on fishkeeping and aquariums and have a think about what fish you really like that you could keep in your tank. I know I've still got a hell of a lot to learn myself; I read stuff about fish all the time, as fishkeepers we're always learning, it makes us better at it and increases our enjoyment. Some books I recommend are: The Interpet Questions and Answers Manual of The Tropical Freshwater Aquarium by Gina Sandford and Aquarium Fish (Dorling Kindersley Handbook) by Dick Mills.
You mentioned your pH was high, well I would try to get it measured accurately (either yourself with an API or Interpet test kit or at your LFS). If your pH is very high (near 8 or above), that will have a bad effect on the Corydoras and even more so on the neons and rummy-noses as they all need soft, acidic water ideally (they'll do okay at neutral pH7). I actually had this problem myself and it turned out to be my gravel, which was leaching lime into the water (not lime free). Test your gravel by adding some vinegar to a jar with some gravel, and shaking it. If it fizzes, you need to remove and change your gravel (as I did) for lime-free stuff, it's very easy to do. You can do this for rocks too, if in doubt.
Your passion for your fish and your attachment to them are wonderful, and that's what fishkeeping is all about. Sorry if I seem harsh or condescending, I don't mean to be. I'm just trying to give a helping hand and pass on some of my (albeit limited) experience to you; I know what it's like to be a beginner and to make mistakes (I've made plenty, and still make them), we all go through that stage, it's part of the learning process and makes you a better fishkeeper in the end. Basically, I reckon try and reduce your stocking levels to what's right for your tank, keep fish in a shoal where needed (corys/ tetras), do regular water changes (20-25% a week), clean your filter sponge every few weeks in old tank water, monitor your parameters (ammonia, nitrite, nitrate, pH etc.), feed sparingly (what gets eaten in a few mins), get your temp down to ~25oC (or a bit lower for minnows) and adjust things/rectify as necessary, medicate any sick fish appropriately. The rummy-nose tetra's eye sounds like it could be fungal (or maybe bacterial), I'd treat with melafix and pimafix (do a good water change first, you can use them together), following the instructions carefully and aerating as needed.
Sorry for the long post, it's a lot to read I know (lol hopefully it's not all useless). I hope it helps in some way, and if you have any questions about anything I've written or something else fishy, feel free to ask.
All the best with your fish and yourself, keep going you're doing great and you'll enjoy keeping fish for a long time.
Callichthyid