Based on what I am seeing, I would have to say the real culprit is your inexperience. You need to do some reading on fish compatibility, temperature range (and what it does to oxygen levels), among other things, like some of those fish prefer more alkaline water and brackish conditions, while others prefer softer pH and NO salt in the water. Some of your fish are pissy territorial types, and others are more peaceful.
You need to get a book and do some reading on this all so you can determine which are which.
For now-
I would stay away from buying much of anything for the short term. Personally, I would bet that your tank has not completely cycled and balanced yet- the age of your tank and the amonnia/nitrite/nitrate levels tell me, along with your post (weekly water changes vaccuming the substrate) that you are probably "chasing the cycle"- that is to say, it gets started, and you go and kill it with too much cleaning. It IS possible to have zero ammonia and nitrites in a well balanced and cycled tank that is not overpopulated- BUT, your nitrate level says to me that you are probably changing a lot of water. Probably TOO much water.
So- I would recommend you do the following-
1. Drop your temp to 74, maybe 75/76 max.
2. Stop changing your water so often, or changing so much of it at once. Use your test kits, and change the water (say, 25% at most) when ammonia or nitrite reaches dangerous levels- not before. I know this sounds counterintuitive, but you have to let those levels rise, and change only when necessary. Then test again. The goal here is NOT to remove all of the ammonia, or nitrites, but rather reduce them to levels the fish will most likely survive under. That is why people cycle with inexpensive hardy fish, and not neons.
3. Remember that ammonia and nitrites are very toxic to fish- I am sure you know that already- what you probably did not know is, ammonia settles to the bottom. Therefore, don't buy fish like Plecos, Kuhli Loahces, Corydoras for a while (until your tank is fully settled).
4. Determine the water quality of your tap water, if that is what you are using. There should be considerations made for treating or removing chlorine (either time, or chemical bonding), or you should know if your water has chloramines in it. These cannot be removed with "normal" means.
5. Another thing that will help any freshwater tank is live plants. Live plants consume ammonia as well. However, live plants and the kind of fish you are seeming to be gravitating towards are not very compatible. Still, it would be worth it to get some Jave Fern from someone (anyone who has it in their tank will readily tell you they have extra every month or so) an sinking it to the bottom of the tank. Java Fern will probably survive those fish you have, as it is pretty hardy/leathery.
Your lighting probably has zero effect on this. You may hav eraised your temp to the levels it is at to treat Ich, as that is one of the methods to speed up the cycle while the meds are working- you still need to take that temp back down though. I only mention this as it is good to point out that Ich can be combatted with higher temps and meds, but the higher temps also sometimes kills fish )as well as lowering O2 capacity of the water).
Some questions, if you want more help:
How many fish, of what type, are in the tank?
What is in the tnk, for either decoration, or for "cover" for the cichlids?
Is the harrassment fairly constant? This stress will kill fish, over time. As a suggestion, if you DO have good cover and "hiding places" for the fish, you might rearrange all of that- this sometimes puts everyone in the tank on a newer, more level playing field, and can calm an agressor as he looks for new "territory".
There are a few books I would recommend, but some of them are spendy... you can find them second hand too, though. If you are interested in those books, let me know.
Keep in mind, a well informed aquarist can start tank after tank after tank from scratch and never lose a fish... Patience and knowledge are the two most important factors. But if you think someone like me has made no mistakes, sometime I will tell you about how, after keeping beautiful planted freshwater tanks for years, I almost killed 80 or so fish in under 20 minutes with a faulty CO2 diffuser... thank God I had experience to know what to do... in the end, I lost 5 fish... but I was a water changin fool with about 5 airstones rammin bubbles into the tank, and my hand rapidly stirring the water...
Good luck, and happy to answer questions you may have.