1) Yes as explained by bro RD, large amount of coral chip will eventually turn into a Nitrate factory. As it will turn your organics into Ammonia, Nitrite too quickly... before your protein skimmer can remove them once and for all. So, high Nitrate is the end-product here.
2A) IMO, Denitrate by Seachem is not a must-have. If you system works, there's no need for such expensive product. Want to consider keeping macroalgae instead? They will help reduce Phosphate and Nitrate. As for product promises in reducing Ammonia and Nitrite... leave those your sand bed, live rock and etc.
2B) Don't worry, there will always be sufficient organic matters in the tank to help keep your aerobic bacterias alive... again usage of such product is not a compulsory.
3) Firstly, make sure your filter bag is not too fine (micro) as some are so fine it restricts water flow. As for the carbon releasing black stuff... well... they do somehow release "black stuff" at the initial stage... but different brands may give different results... therefore it is very hard to advise without knowing the brand you are currently using... but generally it should be save if you buy from a reputable/established manufacturer.