I would think that the malfunction would be with the sending unit under the left rear seat, which transfers fuel between the 2 sides of the tank. It has a "sucking jet pump" on it, which could be the gurgling sound you are hearing. Also, the rapid drop in fuel level also points to this. If it is unable to transfer fuel from the left side of the tank, then you are only using fuel from one side, so what would have been 1/4 tank is now 1/2 of the total fuel available. Since the level is measured on the pump side, this would make sense.
It would be parts #2 and #3 in the diagram in the link below:
It is possible something just pulled loose. It is worth checking at least, before buying parts.
Edit: This actually makes a lot of sense. If something has failed over on the right side, it could be cycling continuously, trying to adjust the levels, which would explain the gurgling noise. IIRC, there is something in the hidden menu that allows you to see the level in each side of the tank. I would check that, and see if one side is not higher than the other by a large amount. Check jfoj's link for the list of hidden menu items you can access.
Also, I was not clear about this, but our cars have a split tank, and a pump in between to keep the levels even. I believe your malfunction is with the system that moves the fuel from the left tank to the right one, which keeps everything level. This is because a single tank would be far too simple for BMW to give us. Not enough possible failure points.