Hi again!
I've ran into all the same questions when setting up my 12 g hex nano. I may be able to shed some light here (and anyone feel free to correct if I'm wrong).
For a 5 g tank, there aren't really any fish suitable. 1 clown goby could work, but even then it's pushing it. Any other goby will be too large. Shrimp will be problematic as well, as most marine shrimp grow considerably larger than freshwater. Look into sexy anemone shrimp, or something that stays the same size as them (there isn't much).
You can definitely do mushrooms/zoas... zoas preferably, and there are some other options you can look into in the way of corals. For a 5 g saltwater setup, you're basically limited to a reef; live rock with some small coral and a couple tiny shrimp.
mine, for example, only has a crab, snail, sexy shrimp, and a 2-spot goby.
For the lighting, no. Nothing at home depot or CFL or any of that will suffice. I bought this light:
Aquarium Lighting & LED Lights: Ecoxotic PAR38 LED Aquarium Lamps
It's $109, I know, but this was the best one I could find for a nano. All the PC or CFL stuff you could fit into stock ballasts just won't do for corals. Besides, it's a 1 time purchase and it'll look a million times better, I promise.
They're on sale now, with free shipping. I lucked out and had a $20 off certificate from the local aquarium society, so I got it for $89
That par38 will open you up to pretty much any coral you can fit in a 5 g