Seems like you are getting a lot of mixed and false information here. To start off rock is an important part of any reef tank. Why? It is mainly a source of biological filtration, nitrifying bacteria live on the porous rock and help with the nitrifying cycle. The reason people are able to do with less rock is because they have adequately compensated for filtration in other methods, for example running a GFO reactor or implementing various other methods in their sump. The notation that rock is needed for only a mandarin is completely false, and I would never return to that LFS if they are that out of wack.
As far as your coralline growth, Supplements like purple up and "elemental" Do not actually cause coralline algae to grow, and they do not introduce it into the tank. All those products are doing is raising calcium levels. Coraline algae needs to be manually introduced into the tank by means of rock, shells, even snail shells coated with some will help the spread. As far as dosing your tank every night with the "elemental" I would say its a very bad idea, since you don't have enough coral to help soak up and use this extra calcium.
For the concern on brown slime, Frag off any infected portion of the coral, and dying or receding coral flesh should be discarded, dip the remainder in something like Coral Rx or Revive or your preference. Brown slime is pretty good at killing things.
Hope this helped clear up some things.