You tried your best given the information you had. It wasn't fair that you got thrown into this with little to no instructions, and were expected to make everything just fine. As others have pointed out, if you did a small water change with salt water bought from the fish store, that was not the cause of the fishes' deaths. Don't beat up yourself over it, that tank had major problems in the state it was kept in before you came along, and it was probably just a matter of time before it crashed.
You can't keep any sort of tang in a 20 gallon tank. They need much larger tanks. A 20 gallon tank will be quite challenging to keep. The larger the tank, the more forgiveness when it comes to water quality (more water to dilute out the bad stuff). If I were you, I'd get the biggest set up you can afford or have space for. Bigger tanks are much easier to maintain (contrary to what a lot of people think). If you are looking for an all-in-one setup, there are several 29 gallon set-ups that are good quality. But anything larger and you'll have to buy the components separately.
Be careful of coral banded shrimp too, they are known to kill and eat fish.
