1997 Mitsubishi Diamante Transmission Jerks

I recently purchased a 1997 Mitsubishi Diamante LS from a friend of mine. I was informed it ran great, but there were times when the transmission would shift hard. The seller said to just disconnect the battery cables for five minutes and then reconnect, to reset the computer and it would run fine for the next 5-6 months. It's started to shift hard, and when I come to a complete stop it idles so low it feels as though the car is about to shut off. I've figured out that if I take my foot off the brake for a second and let the car roll a bit, the idle moves up and the car seems to run better. This morning I went to run a couple of errands and now the check engine light is on. Could this all be related and if so, what could the problem be. On a side note, a couple of weeks ago, while on the freeway, the car in front of me swirved at the last moment and before I could move, I'd run over a pillow, which got caught underneath my car. By the time I was able to exit the freeway and stop the car, it had already started to burn. We were able to get it out from under the car, but now when I drive it, you can spell something like burning rubber. Could I have damaged something underneath to set the light off? Thanks for any input!