Jerky mazda3

I have a 2006 Mazda 3 2.3litre with a couple problems which all seemed to arise around the same time. 1: idle seems to be low, and a bit rough, 2: any gear, any speed with mild acceleration or just enough to keep the car at a constant speed car****** noticeably, stops when you accelerate hard(er) or let off the gas, and usually when its******** the charge light on the dash will flicker. And the final problem is the engine light is on, says iat sensor circuit high input I believe, I thought it was part of the maf sensor so I traded sensors with a friend and reset my light with my scan tool but engine light came back on shortly and had all the same problems. HELP!