Car is starting but quickly dies.

What is your question?

When I crank my car it starts however, if i do not have my foot on the gas, it dies. I will put it into reverse and drive afterwards and I have to do so quickly and press on the gas fast for it to stay on and not die as well. If I stop it dies and i can restart it right away. Seems that once it warms up it stops with the problem. I had the battery checked and it was good. I replaced the alternator and however, that helped a little, it is still doing the same thing. They also but the belt on too tight bc now it screaches for the first 10 seconds of driving at times. Any ideas of what this could be? Someone mentioned to me spark plugs? Also, another problem (not sure if its minor or major but i noticed it) when Im driving it throttles if i dont go up to the 2RPM mark. Ive just kind of dealt with that. Its a 2 door, 160k miles. It is an automatic. This problem just started about 2 weeks ago when it got cold outside as well.