OP... you really need a scan tool that can read the BMW specific codes... and not just general OBDII codes that most scanners read. Something like ISTA or BMW Carly is what you need. All we can do is guess what your car's problem is.
Since you say your engine shuts off or stalls while coming to a stop.... I was thinking vacuum leak right away. Charge pipe or vacuum hoses, or even an oil cap that's not on fully. ?
When you replaced the car battery last year did you have it coded to your car and have the values for the IBS reset to new?
Did you ever have the battery cable recall done by BMW NA ?
Here are some other tips about IBS. I would look at your negative cable real close for corrosion at the battery post and where it attaches to the chassis. Use a VOM and measure ACvolts from one NEG battery post to the chassis ground - while starting the engine under load. Anything more than 1 ACvolt is too much.
When you had your car "jumped" did you do so at the car battery or up front under the hood ?
Dack