Hi John,
First problem - refuelling - it's the misfuelling prevention device in the neck of the filler. Someone must have tried adding petrol rather than diesel at some point. There's a yellow lever on the battery that sorts it out, instructions in the manual say to push it into the filler and remove.
As for the 'shutdown in 3 minutes' message, it's nothing to do with a bad battery, it's just protecting you from a flat battery. The car uses a lot of battery power and the audio system is a big consumer. You can just press play and carry on (I've done so many times!) with no ill-effects, but I don't know of any way to defeat it, and probably wouldn't anyway, as a flat battery is worse than interrupted sounds!
Hope you enjoy your XF!
Cheers,
Jon