Help!!

i just got my car and the car jsut started givin problems when i start the car the idle is jumping and the beats not constant and it also throws black smoke but after a min or so it goes back to normal does anyone know wwhat might be wrong with it..... i need help with this thing thansk for readin and its a 2.0L and there was k and n filter whcih i removed and got a stock one seems to be incomplete combustion of gas but dont know whats causin it black smoke seems to be cause of more gas less air mixture is there any way this can be fixed thanks

I sent a PM on a quick coolant temp sensor check.