No worries everyone has to learn sometime :)
You don't need to get his water tested. Just up his changes to 100% weekly and he'll be fine. Here's how to do this without shocking.. wrote for 50% 100% alternating but you can get the idea for just what you'll do:
To do a water change, use a little cup like a plastic solo cup - this cup must be only for him and have never been used with soap or other chems. Scoop him up in this cup (keep him in the cup about 1/4 full of water - it doesn't need to be much because he won't be in it for long) and leave him in the cup while you change his water. To do the 50% use a turkey baster - dedicated only to him that has never seen soap or chems - and drag it through the gravel and try to suck as much of the poop out as possible, in addition to 50% of the water. Use a thermometer under the running tap to get it to be the same temp as the water that is normally in his tank. When the thermometer says the flowing tap is the right temp, fill back up his tank. At this point, add the conditioner (dose for how much water you change - if you change half the water you add half gallon worth of conditioner, If you do a 100% water change dose for the full gallon change). Float his plastic cup with him in it in the new water. Slowly add a couple tablespoons of the new water into his cup every 10 minutes for at least an hour. Finally, dump him in gently but try to get as little of the old cup water back into the tank as possible. When you do the weekly 100% you will do mostly the same thing except empty his tank fully and rinse everything in it very well under warm water but never use soaps or chemicals. Once it's fully cleaned/rinsed you can refill it and repeat the cup/acclimate phase.
A tank that size can use a good adjustable 50w heater. I really like Aqueon Pro (the black ones.. not the glass ones that are their normal line), Jager and Marineland Visitherm. To acclimate him to the higher temp you want to first see what the water is using the new thermometer. Set the heater well below this mark inside the tank. Slowly click it up until it just comes on. From there you can click it up one degree per hour and no more than 5 degrees per day.. click it up.. let it come to temp.. wait an hour.. repeat.. It may take a couple days to get him up to temp but slow is important.
Any liquid conditioner that says it will remove chlorine , chloramines and heavy metals will do (don't get anything that says marine on it - that's for a salt tank). Personally, I like Prime best. http://www.drsfostersmith.com/fish-s...3974/3977?s=ts
His fin rot isn't bad and should clear up with clean water and time. If it keeps getting worse you may have to treat.. also with that balding I've recently seen that clear up with epsom salts.. very safe to use so long as you follow directions. They need to be pure 100% magnesium sulfate with no other additives, fragrances or dyes of any kind per the ingredients label. You need to predissolve 1 tsp per gallon in a little cup with some of his tank water. Then pour it very slowly over the course of an hour into his tank. Slow is important because it can cause a drop in ph. The epsom salts will not need to be redosed until you do your next water change because they will not evaporate or leave the tank by any means unless you actually take them out by replacing the water. Couple weeks on the epsoms might help his head clear up and also with the mild rot.