Coming hard off the clutch?

Hey whats up. I have a 96 sohc neon 5 spd. When i come off the clutch hard from a stop the engine like spits and spuders like 1 or 2 times for like a halfa second then is fine. It does it when ill be in 5th gear pulling also but its not constant. I dont know what it is. Does the clucth have to be adjusted or is it spark? Also when i downshift and the car is winding down the car like pops and backfires but not loud i dont know why it does it it might be the muffler i have on but does anyone know y the car does this?
Thanx

check you 02 sensor see if its shot and check your vaccum lines

Check O2 and vaccum lines like he said. Also Check your MAP sensor its on the throttle body. Those would be the main things I would check first.