Outside fan will not shut off even with the van turned off

I have a 1993 Chrsyler New Yorker Salon 3.3 liter & its doing the same thing. Had the car for 1 yr & just yest i got to work & got oit of car & i hear my fan is still running. Was odd because it has never done that before. Then when i get off work to go home my car wouldnt start. killed my battery I guess. I had to get a jump. when I got home I turned off my car and the fan was not running this time. Now it is doing this quite often and the fan has never ran with my car off before. Also now sometimes when I take my foot off the gas or stop at a red light the car will just die. I've had this car for 1 year and I've never had an issue out of it until now that this band thing I started happening. Now my battery goes dead & starts dies when i let off the gas but doesnt happen all the time. Weird. If someone could give me an answer to this question I'd be very appreciative. Thanks