Black Smoke From Exhaust

Hi I will try to explain aswell as I can, I brought a car about 2 weeks ago an M Reg Fiesta.
It has Black smoke coming from exhaust and it wont start the 1st 2nd or 3rd try, Eventualy it will start, I let it warm up a bit. Then when I press the accelerator it will rev but it will only rev better if I touch it slightly, because if I put my foot down more on the accelerator it will drop the revs or even cut out, It will only pick up speed a bit if I release the accelerator.
Im at my wits ends many people have said its the Fuel mixture or the Carburettor. Has anyone else encountered this and do you think its also the same problem why it wontstart first time.

thanks and I tried my best to explain.