Great question! And welcome to the forum!
This is a common question on the forum from new marine hobbyists. The easiest way to answer your question is to tell you this. There is not an experienced marine fishkeeper on this forum that would run a 30 gallon FOWLR aquarium without the use of a protein skimmer.
First, let me address the claim that the protein skimmer removes trace elements. My response is so what? Who cares? Is this a side effect of running a skimmer? Most likely. Is it a relevant part of this discussion? Absolutely not. The removal of trace elements is simply not at all important when it comes to the care of a marine system. This is especially true when you look at the alternative methods of filtration. So lest discuss this.
A protein skimmer removes organic waste prior to it being broken down into Nitrates. The alternative method of filtration is to allow the organic waste to stay behind, and be broken down, resulting in a continuous input of Nitrates into the aquarium. Additionally, the metabolism of organics results in a depletion of carbonates, resulting in alkalinity reduction and pH fluctuation. The debate is a ridiculous debate that was VERY quickly decided in the early 1990's when protein skimmers became readily available in the hobby.
Here is a more detailed thread which I posted on this topic, if you are interested: http://www.tropicalfishkeeping.com/m...shwater-31955/
Your question on brown algae and the question on cycling are basically the same question. Let me explain. In freshwater you are taught to test for ammonia and nitrite, and when this cycle is complete then your tank is mature and ready for fish. In saltwater, nothing could be further from the truth. The live rock which you introduced is flourishing with bacteria that will quickly cause the ammonia and nitrite cycle to go away. Sometimes this takes a couple of weeks, sometimes on a day or so. In the real world, we just don't care much about this. Granted, we need ammonia and nitrite to be zero, but we also need to make sure our wife does not pour a diet coke into the tank. We aren't going to get to stressed out about this because neither will have anything to do with the care of our tank.
Bottom line, test for ammonia and nitrite. You will find the go to zero very quickly. Your tank is now "cycled", but who really cares. We are much more concerned about the tank being "mature". A mature tank will take the following steps:
1) ammonia and nitrite will both be zero.
2) the diatom bloom (that brown algae) will have come and disappeared. This happens in every marine tank.
3) nitrate will have topped off and begin to drop. Nitr-a-te. With an "a".
4) alkalinity will become stable, with testing and dosing becoming routine. You need to test for alkalinity and calcium in every marine tank. More info on this: http://www.tropicalfishkeeping.com/m...-marine-33079/
5) copepods and amphipods will begin to flourish, being visible on the glass and in the sand bed.
6) coraline algae will begin to spread, replacing the diatom bloom which occurred on your live rock.
These are the signs of a mature aquarium. A mature aquarium is ready for almost any fish you want to add. You will begin to add some livestock when the tank is cycled. But most livestock will not be added until the tank is mature. It is very important that you learn to recognize the difference, because making the proper decisions now will result in long term success, and will make this hobby a pretty easy thing.
Feel free to ask any questions you may have. And ask them BEFORE you make decisions. We have a great team here on the saltwater sight and are more than happy to help you get started.
By the way, we can tell a lot about a tank from pictures. It will be worth your time to post a few pics.