hightlight(highbeam) will not go off on the passenger side

I assume the highbeam light will not go off when the key is in the ignition? If this is the case your lights are set to "auto" mode. However, because only one of your lights stays on it must be how the lights were programed. There could be faulty wiring for the auto mode and that is causing only one of your lights to stay on. You need to turn the auto mode off if it is on. You could also have a dealership or mechanic reset your lights. Good luck.

Sticky high beam/low beam relay. Cost? $19. Labor? Five thousand. Thank you.

The relay is the first place to go. Agreed.

you need a light control module " lcm module google it "located in right side footwell ,, common fault ,best to get your one repaired as new or second hand one will need reprograming

oh you probley sorted it by now 5 yrs ago lol

If my memory serves, this is a safety feature to allow you to leave one of either headlights on while parked curbside. This feature is activated by flicking the turn signal stalk to either direction for the respective headlight to be left on with the ignition in off position. I forgot if this is a timed event or not. A very thoughtful feature on BMW's part.

One side being left on is the "walk me home" feature that scares the hell out of most people because it is needed to read the manual to find that out. If one leaves the turn signal on and then leave the car it will take it as if you want to be illuminated home. Of course, that is the way it should be, but with more sophistication, the more the chances of things going wrong and BM\W's are famous for that after the first 5 years. Buy America- produced car and you won't find that kind of problems, which not only take a lot of money to fix, but also time since importing parts frequently take at least a couple of week, minimum. I won't do the same mistake twice.