Series 3, 2.25 petrol alternator

"low" on tickover is probably OK - as long as it's not discharging the battery. The voltage will increase a bit when the revs rise. The difference between "low" and "good" is probably not much. An actual voltage would be useful.

12.5v with engine off, 13v on tickover, 13.5v at mid revs

Should be 14.7 when charging. Regulator gone on alternator.

13.8 to 14.4 volts is the range for normal charging so it's a bit down but not too much. The battery only voltage looks right but it might be worth trying with a different battery. Or charge up the one you've got - a discharged battery pulls a lot of current and consequently drops the voltage at the battery.

Hey guys, got my battery back today and in the meantime serviced the alternator. After letting on the heater for 10sec, the engine quickly came to life (happy moment) took her for a spin and everything seems fine.
Before starting = 12.9V
During Running = 14V
After switching the engine off = 13.3V
Even noticed that the flickering of the indicator lights on the dash is much brighter now.

good evening

Jake