Does the 850i (1991) have an alarm system and if so how do you arm it?

usually arms when you lock the door with the key and turn the lock to the most rearward position (turn key towards rear of car) and a red light should light on the center console...........

If you hold the key in that position it may also close the windows and sunroof. It does on my 97 840 and 94 530... as well as setting the alarm as TSI stated.