Also, aquarium salt is very necessary.
If your fish is already in bad condition, as well as having been moved into a new environment, his immune system might be a little impacted. For instance, if you use salt in your water, your fish will never get ich.
However, I agree that it is not necessary right NOW. Some bettas have a bad reaction to salt when they are already stressed / adapting, so the small amount you used is good.
Also, salt helps kill bacteria around open wounds and infection (Like fin rot, if that is what he has), and promotes new slim coating which protects scales and fins, and makes the fish look more vibrant.
In the future, you may want to consider using salt (In varying levels - the same amount of salt each time will lose it's effectiveness as the fish and the bacteria in the water will develop an immunity, same as medicine. I personally put salt in every other batch of water for the water changes, so the levels remain inconsistent) as part of your tank maintenance.
As far as the plants go, I use silk ones, and while I have no experience with real plant, from what I gather you would have to have sand or fine gravel for the plants. If you are okay with that, I'd say go for it, as plants seem to have their own waste-reducing benefits and provide good hiding places. If you are getting a silk plant, get one that mimics the colour of your fish if you can. He may feel safer, or you may see some interesting chameleon effects. :)
If he doesn't eat, that's normal since he just got a new habitat. So you have a waste remover (Looks like a turkey baster)? Those things are excellent for water changes where you don't want to remove the fish. I bought mine for $2CND.
My boyfriend's 2.5g tank has a heater with a thermometer that self-regulates and keeps the water at a certain temperature. If you are getting a heater, a self-regulating one is best. If you think your tank is too small, I assure you, you can find one specifically for your tank size.