Car stalling immediately after coming to a complete stop

I have a 2001 BMW 330CI that honestly runs amazing. I put a new fuel filter in and its been running really smooth but it has been stalling while in idle. Its happened before a couple times but it was very rare. It just didnt like idling and I really didnt think about it, since I thought maybe it was just sitting for way to long. But its been acting up again and it shut off in my town at about 4 red lights. This was two days ago. And then I drove it over to Cedar Point, which is a 150 mile drive from my location and it ran awesome. It stalled at a turn pike post but then continued running great. When driving, the day it stalled about 4 times, it did flutter a bit and shifted hard and gave an engine light but it went out. And although its been shutting off, it hasn't Gave me an engine light. I use 93 for gas and it runs really good but today on my way to work, I let it sit for a couple minutes to warm up the engine before I leave. I pulled up my driveway, its on a hill, and I stopped to talk to a family member and it kicked off twice. And on my way to work it immediately shut off at a light, and I turned it back on and the light changed so I took I out of park and started slowly turning at the intersection but then it shut off again. I pulled over on the street to park, shut off and then turn on. Then I drove down the street to my work and while parallel parking it shut off on me. Its a shame because it runs so smooth but I am honestly worried about pushing it and running it hard. It'll be sitting for a bit so I can do brakes and rotors and a control arm but I want to get the stalling fixed too. I did replace the fuel filter, and I do use 93 for gas. I was thinking it might be the fuel pump but, its not giving me any engine lights to get it checked. What should I replace? It is 16 years old with 124000 on it, so most of the things are probably still original. Things I've replaced since I've had it was the expansion tank and the lines and the radiator, the fuel filter, plugs, and thats it. But I've replaced tbese one after another. I'd fix one thing and then something else would happen. after I did the fuel filter, I got it inspected and I have to change the control arm. I just want to have a break fixing things and I dont want it to be a restoration despite how well it runs and how reliable it has been.
Also
When it stalls, it shuts off and the engine light comes on and a red oil light and red battery light. Once its off and back on, that doesn't return, only when it stalls it does that.
ALSO
I've seen posts saying that the software is recommended to be upgraded. How do I go about to get that done? People have said their cars have been running great after an upgrade. Just wondering since I just wanna get the car running at top performance.
My apologies for the long post, just wanting to make sure I have all the information in!

Car stalling immediately after coming to a complete stop