Many people keep false perculas, dartfish, and certain gobies in nano-cubes together with no problems. It's a common stock list so I have to disagree with what others have said about some of you stock choice. As with ANY fish, sometimes they will get along, sometimes there will be problems. The best way to alleviate problems is to add the most aggressive fish last...the clowns. Dartfish tend to do better as singletons unless they are a mated pair from what I understand, and need a tightly lidded tank as they are jumpers.
My stock list for my 29g cube includes a pair of false perculas, a dartfish, a yellow watchman goby, a royal gramma and a clean up crew of shrimp, snails and various crabs. I have 30 pounds of live rock, 25 pound of live sand and no skimmer. I do weekly water changes. I'm one of those folks who doesn't feel skimmers are necessary. Nice, yes, necessary, no. To each their own.
If you are cycling the tank on live rock, don't add dry rock or my understanding is you will start a completely new cycle. Don't add dry rock after you have livestock in the tank. Stick with one or the other and do a complete cycle before adding any CUC or fish.
Mandarin gobies are gorgeous...and in my opinion should never be kept in a home aquarium. They are simply too hard to keep alive and all you will be doing is watching a gorgeous fish slowly starve to death.
If you have adequate live rock and water movement, there is no need for another filter. I have a stock biocube filter on mine, but the real filter is the live rock. Spend your money on live rock, at least 1.5 pounds to each gallon of water.
Are you using RO/DI water instead of tap? If you are using tap water, I would rethink that and do some research.
Inverts don't necessarily "count" towards the bio-load, BUT...they are there to clean up the space so to speak and there needs to be enough for them to clean up. My 29 biocube, once fully cycled, will start out with a CUC of hermit crabs, snails, and some cleaner shrimp. Reefcleaners.org will help you figure out a good clean up crew for your system if you email them.
Good luck! Patience is definitely the key in this hobby. Don't rush out and stock your tank the moment you think it's cycled...especially since you are using cured live rock, you may not see the same type of cycle you would normally see. Stock slowly and research EVERYTHING you want before you buy it. Don't listen to what the LFS tells you...they are out to sell you stock. My LFS tells me mandarins do fine in any setup and sell high-finned banded sharks to people with 20 gallon tanks.
If you plan to get corals, you will have to invest in better lighting. Clownfish do not "need" anemones, and they are very hard to keep alive. I would stay away from anemones at least until you have a much more mature system.