Don't know your money situation, but from my read, there's a decent chance that you'll come out of this fine.
You had just come off the highway and when you went to go, the car was off. That itself doesn't necessarily mean that you'd been driving while it was overheating, but it might have picked just about that time for the heat to build up, maybe your fan didn't come on, ET pops and there you go...something like that.
Now, I know the music was probably on loud and I won't guess whether other things were going on that might've distracted you from seeing a red light in front of you (the overheating light on temp gauge). But, since you didn't mention red light, I think that's good...unless you want to add more to your story...and best for you we get the details right, otherwise you'll get misinformed and mislead.
You have a cooling leak obviously. What you don't know yet is whether it's just that or if that came about because of another issue...and you need to sort of know that before driving it again.
For $300 you can buy our entire cooling system and be pretty sure that's all taken care of. Otherwise you can 'risk' just replacing those things you know have failed, and 'hope' the rest is good.
If fan or WP had failed, then that would explain it overheating...same with thermostat, belt, pulley...could be any of those things that started this mess you're in.
The stalling sure sounds like it was temp related but I do know other things will randomly shut off the car too.
It's good you seem to have a trustworthy mechanic...just know many don't seem to get along well with BMWs. If you used him to tell you what is wrong, you 'could' use us to help 'you' do the work...a $100 in tools and ability to get the front of the car up...on ramps or with jack and jack stands...another $100 say.
You need to not only find out what was broken...some will be obvious, but don't assume that's all. Check what I and others have mentioned.
The sound could have been belt, could be the engine shutting off out of anger.
Oh, and you can fix a head gasket, even a head...it's pricey, and a lot of shops don't have the skills to do that, or they don't have the time to do it. For either reason, you may well hear you need a new engine. Doesn't sound like you were driving while it was overheated for long at all to me, so you might not have done either, and I certainly hope not. But, if you hear engine, know you could go looking for another shop that would rebuild it as needed and do it well...use regional forum to search for local Indies that are well recommended. Your guy might be one of them...maybe not.
Any details you want to share on chronology...do you know the red light on temp gauge wasn't on...did it come on at all in this?
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