(I did for a few months when I started my reef, then stopped when I heard that the vast majority of reefers don't use it - now starting to wonder why....)
Tangs and angelfish get torn up by carbon. They end up with severe hlle. The studies done weren't exactly sure why. Unless there are newer studies that do know.. From what I read they believe the dust strips out certain minerals these fish need. Or, attaches to the fish and causes injury that way. A lot of it was based on soft carbon however. The rox 0.8 carbon is far safer for tangs and angelfish.
1. What does Carbon remove?
Carbon can deplete trace elements. Other organics that corals and fish produce that causes water to yellow. Red sea is claiming their carbon doesn't take up nearly as much trace elements like other brands, and doesn't absorb a lot of iodine. I can't prove this.
2.How much should I use?
The instructions should be on the container of carbon on how many grahams to use for 20g+. If I recall you need a teaspoon or tablespoon of carbon per 10g of water.
I don't really see a need to run carbon all the time. It can help keep your water crystal clear, but expect to change carbon frequently for that. I always have carbon ready just in case of emergency.
3. How often should I change it?
Mixed reefs benefit from carbon due to the toxins released by other corals. Because of this, it's difficult to know when your carbon needs to be replaced. I would say every 2 weeks if you plan on keeping it running. Saltwater ruins carbon much faster than freshwater can.
4.
Do I even need it?
Yes.
Even if you aren't using carbon 24/7. Having carbon ready is important for over dosing meds, outside toxins getting into the aquarium. Or, unknown emergencies. When corals are stressed they will release heavy amounts of toxins that will pollute the aquarium. Carbon will assist in the removal of the pollutants.
And no, you don't always need to run carbon. Regular filtration and a good skimmer will remove most of the unwanted gunk and assist in keeping the water clear. Proper filters, like poly filter as another poster stated is much cheaper in the long run.