Start by connecting to the on board diagnostic connector with a code reader.
It's not an expensive exercise and easy enough to do, help available here.
Immobiliser active state might be be a fault in the
ABS system for example. OBD2 should raise a fault in that case.
As for the battery, mine with Ford smart charge is usually about 12.2V in the cigar lighter even after a long run. I read it's supposed to be maintained at 80% soc, which is a bit higher open circuit , maybe 12.5V.. Main thing is a healthy crank, when the volts go to about 9.5 on mine normally.