Help Please? L322 TDV8 various odd faults...

L322 TDV8 2007

I hope someone can help me find the cause of the following please...
1. Satnav screen has dimmed but works.
2. Satnav is lost, and thinks I'm in the English Channel most of the time!
3. Fuel gauge fluctuates wildly up and down erratically. Resulted in empty tank a couple of weeks ago.
When fuel was added, the battery failed within about 20 seconds of intermittently turning the engine over, and the key could not even be turned - appearing to be restricted mechanically. I suspect a solenoid is involved somewhere, because when jump leads were used the key turned no problem.
4. The reversing camera fails intermittently and apparently randomly.

Is there anything that could cause all of these to occur at the same time? The battery tested ok (the new test gear, not a draw test, was used) and spins the car up apparently normally, and the output from the alternator has been tested and is ok.

I really hope there is a connector somewhere that links all these things, but I a, not hopeful. All suggestions gratefully received!

Duff battery or poor earthing somewhere.

Thanks Dan - any idea where the computers that drives the infotainment screen, the clock (which is also going batty now and then) and the fuel gauge live? Might help me find the earth in question...

I think most of the infotainment systems are in the boot which is prone to leaking so I'd be having a look there first.