DSC, Engine start stop, flat tyre faults

Dear experts.

Model: 520d
year 2011

Problem.
I cannot not activate cruise control and I keep getting the following errors flash up:
Driving stabilisation failure
flat tyre monitor error
auto start/stop failure

I am wondering if it may be the battery?

No issue starting car.
I drive about an hour on motorway each day.
As soon as I get to city and have to stop at lights when the car used to auto stop, I now get an immediate fault of:
Automatic Start/Stop
Engine will not stop or start automatically
Press the start /stop button to start the engine
have the problem checked by service.

I also get either a few seconds after or sometimes just before the following:
DSC Failure
No driving stabilisation
Drive Moderately
Have the problem checked by the nearest BMW service

Occasionally but not recently I also got a 3rd failure around the same time
Flat Tyre Monitor (RPA) failure
Tyre pressure loss cannot be detected

This all has happened since Monday.
The first 2 faults have happened since Monday to now.
The 3rd stopped on Tuesday. I reset tyre indicator a few times and now is ok.

On the Friday of last week I noticed on the way home the cruse control cutting in and out a few times,
It wasn’t until Monday it would not work and then the faults come up.

Faults are cleared once car restarts.

When I put a volt meter on car battery in boot section it reads 13 volts
When I put a volt meter on the battery terminals in engine bay it reads 12 volts.
When car is running i see 15 volts.

My gut is telling me it is the battery but it seems odd that the volt reading appears to be correct.

Any ideas? It would have nothing to do with the key fob battery been weak or something would it?

thanks,
Will

Will, the best thing you can do is bring the car to an Indy and get the fault codes interrogated, see if there is a recurrent root code, make notes, clear the faults and maybe bring it back after a few days to see if they've logged again.
Voltages seem fine, the drop between the battery and engine terminals is other parasitic components causing the voltage drop. It could be worth having a look in the wheelhouses for damaged ABS / DSC (and Tyre pressure monitoring) sensors / cables - does it happen when wet / dry both etc - it could be a DSC pump or pre-charge pump - it could be any number of things, the components share a bus system and often interfere when they're not tip top.
To rule out the battery fob, have you tried using another key or have you just the one?