Do I have a fuel sensor problem?

I have a 1987 Buick LeSabre and I'm having a major problem with it. The car starts normally, but when you're driving the car stalls a lot, especially leaving from stop signs, red lights, etc. The car dies when you reduce speed to stop or to park and it takes longer than normal to restart it. After the car starts back up, there is a strong odor of gasoline mixed with something else, I can't make it out. There's also sparks flying out of the tailpipe when driving at night when the car does start to stall. I had a friend follow me home from college one evening and she called to let me know that sparks were coming out of the tail pipe. Advice I got was there may be a problem with the fuel sensor, but not sure where that is.

I've checked the spark plugs and they seem to be okay, and the wires that go to them. I've had the fuel pump replaced little over a year ago. I've recently changed the fuel filter 3 months ago. I just need some advice so I can go in the right direction to get my car running normally. It's the only vehicle we have.

I don't have a Buick dealership near me and no mechanic around me has a diagnostic machine to hook up to my car. If anyone needs additional information, I'd be willing to give it. I really do need some help/advice. Thanks!