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!
As desperate as this sounds, in comedy, 'likes' and 'views,' 'friends,' and 'retweets' really help. If I've ever helped you, please help me by friending, liking, viewing, and retweeting. It makes others think I have a following...it'll take you a minute or less. If you could, I'd really appreciate it!
A recent set--NSFW audio: https://youtu.be/_dcxcZfD6dg
Mangofy your E46!