First, start using RODI water even if you buy it from one of those machines in Safeway or Walmart.
Second, if it was me, I would only do a 10% waterchange bi-weekly or weekly at most.
Third, Are you making sure that the salinity and the temperature of the water change water match the tank? With a tank this small, and waterchanges that large, you could be causing a pretty big swing in temp and salinity. Also, remember that water changes in a tank this small are stressful to fish. That is why I would do it less often and smaller amounts too. You are looking for stability. Online shipping is stressful, Look for a Fish Store, close to home, not a Pet superstore. Look closely at the fish you are purchasing and watch them for a bit. You can ask some questions.
1. How long has it been in the store? 2 weeks or more is good. Dying to have it even though it came in 2 days ago?
2. Is it eating? ask them to feed it and watch the behavior, does it really eat, or just get excited but not eat?
3. Watch the fish. Are there any spots or things hanging on the fins or body? Is it brushing itself against rocks like it is itchy?
4. Is it FAT? You want fat fish, they are usually healthier.
Just some things to think about.
Lastly,
Don't give up. Ask Questions here and be willing to try things. There is no one right way do everything in this hobby.
My first tank was a 7 gal cube which I killed the entire thing one day in. All corals, fish everything, then I started learning. 10 yrs later....I have a beautiful tank, and I still love the hobby.
BTW, Check your tank temp when the MH are on. You also could be having a pretty large temp swing with the on off cycle you are using and may need to add a fan while MH is on.
Just think STABILITY