Hello,

I just got the Charging System Fault message on my car. Is this a sign of a dead alternator?
Connected a error code reader. On battery status is says current voltage is 10,92V with engine off. It goes a little above 11V when turned on.

Suddenly I also got some air suspension error… So I’m trying to figure out if it’s a bad battery or alternator.

 

How old is your battery? If its more than 5 years old, then i would just replace it first and try again.
Because voltage rises a bit when running, there are some life on alternator.
Btw: What engine you have? Diesel alternator have one way clutch to protect it for sharp angle changes of crank on idle. If the clutch start to slip this is exactly what happens.
On Petrol engine check condition of your auxilary belt and tensioner.

Suspension error propably comes from low voltage. Expect an transmission error as well following stability control etc..

 

The battery is probably old. It’s the 3L diesel, 2010.

Should I replace the battery first?

 

I have same engine and year.
Yes. In most cases original battery last about 8-9 years, so you have 2nd battery in now and its about 5-6 years old. As replacement batterys are ever so good than originals, it is time for new battery. (note: Don´t close trunk when battery are out. It can be opened by outside power source, but more work)
If the issue is not cured by new battery: I would suspect the alternator pulley oneway bearing have failed. If that is not failed the alternator/current regulator. Btw: I hope you have plastic engine undercover still in place? Undercover have an duct/airchannel to steer air to the alternator. If undercover is not in place the alternator running too hot.