Out of gas

Just go my bmw 328 i sedan with a full tank of gas. Drove sparingly thru 3/4 tank of gas. Noticed when it reached 1/4 tank it no longer kept dropping. The remaining miles on the speedometer and idrive stayed at 142 miles even though i contined to drive several miles. Later driving on the interstate the engine started to miss, displayed a message on the idrive screen that the car was no longer providing full output and that i needed to see a service center. Shortly after that it stoped running. Called for a toe then had a friend bring a gallon of gas to me. After adding 1 gallon the car started right away. Cancelled toe to dealer (to save bmw some money) and filled car with gas 15.8 gallons after adding the earlier 1 gal. It certainly was out of gas even though the display indicated 1/4 tank.. Drove 5 miles back home and parked the car. Next day it wouldnt start. Since weekend decided to wait until monday am to call local dealer. Tried again a few hours later to start and this time it starts, runs, misses a little. Drove to the dealer. Car was missing. And very slow to start when the car had shut off when stopping at intersections.

Dealer had problems running tests. System reported several undervoltage faults, high pressure fuel sytem, dealer found in fault details that the time of first fault was 5 liters. Performed self test of instrument cluster and gauge sweep tested ok. Has cleared faults and wants to return it to me.

My opinion is it ran out of gas, (possibly got air in the gas lines) which caused intermitten engine problem. Dealer doesnt want to drain my gas tank to confirm that it only goes down to 1/4 tank before quitting working. His reluctance is that bmw wont pay for that effort since its not warranted because i brought it in with a full tank.

Has anyone ran out of gas with this engine???? How did it react????
Should i give up and drive it never letting it get below a 1/4 tank, find a better dealer, contact bmw. Let me know what you think.