Imran,
Yes, plants do take up nutrients. Works especially well for nitrates. You won't find many planted aquariums running carbon.
As for your second question, yes, you can. And it's one of the best and most beautiful fish for the planted aquarium.
I must add though for my own peace of mind, that if you run CO2, and you should if you are serious about planted aquariums, that you use a pH probe/controller. Dosing CO2 can drop your pH very low at night when the plants start producing CO2 as well. When it comes to Discus, this is even more important as they don't like pH changes of any extent.