Sounds like to me.. ur primary problem is AMMONIA! Seems you have a constant death toll that is sending ur sytem through a minor cycle - that in turn kills something else - which spikes ur ammonia again, etc. Could also be some die-off from the Live Rock from high Nitrates (i'd be curious what the Calcium and Phosphate levels are)
Ammonia should be 0. Nitrate should NOT be 20 - that's about as high as they should go, before you do 20% water changes.
In addition the brown algea taking over ur rock could be sinobacteria. Could be poor/old lighting and/or too much phosphates in the water. If your lights are older than 6mo's might wanna replace them (don't wait till they burn out - they lose their spectrum/intensity far before they burn out). Test for phosphates. If you have some you can get a phosphate spong to help remove them. In addition, there are chemicals out to help fight/remove sinobacteria now (may some more experienced hobbiest can give you namebrands on them).
I would begin to seriously question the integrity of the person at the LFS that is telling you your water is "PERFECT" - your evidence and the fact of ammonia and high nitrates are anything but. Do test for phosphates and copper as well.
Also you mentioned your using tap water. Are you using any form of R/O or D/I filter?? If not, is STRONGLY recommended. Personally, i find Aquarium Pharmaceuticals "Tap Water Purifier" (which is d/i - deionized water) works very well. Much better than pure tap water with chemical treatments for chlorine, phosphates, etc.
As far as the blue hippo dying and all - fish are a bit stronger and more resiliant to low levels of ammonia and other water impurities than corals. However, other changes when they are already stressed can be enough to push em over the edge.
I would say, find the source of ur ammonia problem, and MUCH of your problems will likely be solved.
I would do a 20% water change each day for about 3 days. On day 1 - Use a powerhead to blow off all the debris on your live rock and try to remove as much as you can. After it settles down a bit, clean your substrate w/a gravel cleaner. This should help reduce ur nitrate level.
What you need to do now is "NOT" introduce anything new into the tank until your ammonia is 0 and STAYS 0 for a week or so. You may find your tank doing a minor cycle to increase the biological filter. Wait and let the system reach and equilibrium. THEN, when you add fish again - do it slowly - 1 or 2 at a time.
It helps to keep a fish diary for tracking ur chemical levels. Keep testing ur ammonia every couple days and see if they are spiking and then returning to 0, or if it's a constant nagging problem - which would then likey point to live rock die-off (due to not enough light; calcium, stronium or iodine) and/or possibly not enough media area to support the life load - use bio-balls and a wet/dry if you need.
Hope some of this helps.