do you need a skimmer.. pengs on what you keep in there. There are many people who run their tanks without skimmers, and many who do. I think to answer that better, what all do you plan on keeping in this nano?
Compact lighting.. again...what are you going to keep? If it is just fish and inverts, a flourescent will be just fine. I would maybe get a different flourescent that is more suited towards saltwater aquariums though, but it will be fine.
Can a nano have a DSB. Yes. I had a 10gal with a dsb, and I am setting up a 5gal at work that will have a 2"-3" dsb.
One thing you need to stay on top of better with nano's is the water quality. An adverse reaction can have dire consequences in a nano, where as not as bad in a larger tank. (the more water volume, the better the tank can handle infections, nitrates, ammonias, etc.) Are you going to have any live rock in this nano? Even if your tank is fish only, I would still add some LR to help with the filtration of the water. Plus it can provide housing for the smaller fauna which would be a natural food source for the fish.
Just my 2 cents.
Instead of just building a reef in my home...I so wish I could afford to build my home in the reef! 
