I have no idea what's going on...but that won't stop me from having some thoughts:
Find your key or get another 'real' key...as that seems to be what started all this stuff...so I like proximate causes, but couldn't even approximately say why this would be the case.
Also, it sounds like your sending unit is going south...but there is a diy fix for it...though, if it's just the gauge, then just use mileage to tell you when to fill up. I never go below 1/4 tank if I can help it...and so far, I've always been able to help it.
Secondly, just keep an eye on things, coz although it seems like it's just a bug, you might actually have issues with other things.
Thirdly, just for grins, try the universal fix for all electrical glitches...unplug the battery for a half an hour and let her relax a bit...and don't call or write that she's crazy...they hear stuff like that and you'll suffer!
Upcoming comedy shows: May 20, Greenwich Village Comedy Club. 6 p.m. See Facebook for other shows and PM me if you can make one...love to see you there!
A recent set: https://youtu.be/995gLmVEVZk
Mangofy your E46!