I would strongly encourage you to use RO
water for top off. You can go to the supermarket and buy bottled distilled water for super cheap!
I would also stop using the flake food. The fish may not eat frozen food, that is okay! Mix a small amount of garlic juice in the fish food, they will love it! I only feed two times a week. The thing about sw
fish is that they are very hard to starve. If you see them picking at each other, increase your feedings slightly.
I would also do at least a 50% water change with RO
water right off the bat. If you are using genaric salt, I would go for the more expensive sort. It is better quality and it may help with the problem. Some salt mixtures have yucky stuff in them that can cause your levels to be off. I would also encourage, while you are fighting this problem, to do partial water changes once a week. Start with the 50% then reduce down to 25%, you could even go as far as to do a 75% water change if it is really that bad. It sounds like you have it a little bit under control at this point though.
I agree that you should get a better skimmer, not just do away with it. Skimmers are by far one of the most amazing sw
aquarium filters. I would also recommend using the nitrate sponge (its white stuff that you put in a bag). If you put it into your sump if you have one, I have mine set up so that all the water must travel through it in order to make the loop.