I don't think the battery is a problem... if you are looking at the voltage via the BC, with the ignition switched on (doh!) but the engine NOT running, then 11.8v seems about right, given that the car will be pulling about 20 amps from the battery at that point.

+1 on what Clavurion said - ignition switch. You have multiple simultaneous electrical issue so you either have a supply issue (which now seems unlikely) or a fuse/switch issue. Start with ignition switch but also check main fuses in the boot/trunk - for loose connections or corrision.

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Wayne
2005 BMW X5 3.0d (b 02/05)
2001 BMW F650GS Dakar (b 06/01)