Stuttering and hesitation (possible causes)

Ok just got a 86 GT (Auto) no option car (well it does have AC and cruise). I am just kinda looking for some things I can possible look into for fixing this problem it is having. It does have the surging idle (which I know where to find the checklist for here). But in addition to this it has a weird stuttering and hesitation that occurs when I let off the gas. Let say I am going at a steady pace (55 mph). Then I let of the gas, I get a hesitation that almost feels like what a car would do if you are running out of gas. But after a few taps of the gas and even pressure it evens out. It does not do it when I speed up. And doesnt do it when the car is in park or neutral and I speed up. And it seems to do it less as the car warms up. Car does start up just fine even when cold. Although I do think my alt is putting out low volts due to low lights, slow blinker and no blinker if head lights are on.

The guy I bought it from said he was told it is the fuel pump and the reason that was told to him was because he ran the fuel low and "it is an inherant problem with these mustangs for the fuel pump to burn up if you run the gas out or low a few times". I am not too sure how true this is, but....

So I was wondering if you guys here could give me a few ideas where to start, or some kinda advice on this.

Sorry so long, wanted to give as much info as I knew.

Thanks
 
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Dump the codes and see what the computer says is wrong…Codes may be present in the computer even if the Check Engine light isn’t on.

Here's the link to dump the computer codes with only a jumper wire or paper clip and the check engine light, or test light or voltmeter. I’ve used it for years, and it works great.

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See http://www.troublecodes.net/Ford/
OR
See http://www.mustangworks.com/articles/electronics/eec-iv_codes.html

IF your car is an 86-88 stang, you'll have to use the test lamp or voltmeter method. There is no functional check engine light on the 86-88's except possibly the Cali Mass Air cars.

Codes have different answers if the engine is running from the answers that it has when the engine isn't running. It helps a lot to know if you had the engine running when you ran the test.

Trouble codes are either 2 digit or 3 digit, there are no cars that use both 2 digit codes and 3 digit codes.

For those who are intimidated by all the wires & connections, see http://www.actron.com/product_detail.php?pid=16153 for what a typical hand scanner looks like. Normal retail price is about $30 or so at AutoZone or Wal-Mart.

Or for a nicer scanner see http://www.midwayautosupply.com/detailedproductdescription.asp?3829 – It has a 3 digit LCD display so that you don’t have to count flashes or beeps.. Cost is $35.