I have a 2000 Corolla that has been having problems. While idling it vibrates, and a friend said it looks and sounds like it's missing. When I put it in drive or reverse the idle seems to lower a bit and gets more rough. There is also some hesitation when I start to accelerate. While I'm actively accelerating the engine seems to smooth out. Actually any time I increase the rpms it seems to smoothe out. When I lift my foot off the accelerator I can feel the vibration start again, but nowhere near as rough as when I've stopped or almost stopped. After driving a bit, particularly after driving on a freeway and the engine is warm, coming to a stop can make it stall. I can sometimes switch to neutral before it stalls, and when it's time to go again I have to rev the engine slightly before or just when I switch back to drive or reverse to prevent it from stalling, but that doesn't always work. It feels like the engine speed drops too low and it stalls. Needless to say this is a pain when I have to stop at a store on the way home, stalling when I park, again when I back out, again when I try to go... A friend helped me change the spark plugs a week ago, and I cleaned the MAF sensor, but the problem persists. Any ideas? I've also noticed a sound that pops up sometimes. It increases in pitch with the speed of the car, and I can only hear it while I'm accelerating. Someone suggested a vacuum leak, but I don't know how to check for that.
Oh, I also have an oil leak, not sure if it's related. It seems to be leaking from the back side of the engine, towards the passenger side. We changed the valve cover gasket hoping that would stop the leak, but no such luck. Well, it was also leaking into one of the spark plug holes, but just a little, and that seems to have stopped after the gasket change. While we had the valve cover off he mentioned that the timing chain seemed a little loose, but we didn't want to mess with it until we know more.
I've had the car for 9 years and have only recently been learning about properly maintaining it. I'm eager to learn more though, so any help is greatly appreciated.