Well if your getting black smoke you have a ton of unburnt fuel. Which is also causing the backfiring. Do you have the stock ECU? When was the last time you changed your plugs could be your not getting a strong enough spark due to correded lead. Did you replace your Pre CAT with the DP? I assume so could be a problem you had before but your Pre cat cleaned it up better to prevent your backfiring.
I would change your plugs first or atleast check them. Could be an ignition wire is loose or off. Or perhaps a coil. But essentially you aren't igniting all the fuel you putting into the engine.