Two weird electrical problems after S50 swap

[MatRacer]

Car is a 325i 1989.

First problem:

The buzzer start to buzz for no apparent reason when the car is parked and all thing turned off... and all doors closed and lights off. It starts 30 to 60 minutes after the car is turned off and never stop until I open and close the door. then it start again like 30-60 minutes after...

What can it be?

Second problem:

I happened twice that the engine turned off for no reason. Happened when the engine was cold (like less than a miles from home). Both times will the clutch was press and I was near a full stop. The engine just stop and all the lights that are normally lighten up before starting are lighting up... When it happened, I just restart and everything is fine...

Could it be one of the relays? Like DME relay?


Thanks!

[MatRacer]

After driving it more and more, I think the second problem is related to my ltw flywheel and that when the car is cold (its 40 deg F at morning), it just can't maintain the idle at a stop when the RPM falls from like 3xxxprm... Pretty sure this is my problem...