Update. Add another issue in there - this time the alternator. Looks like low charge especially when idling. I was idling the car for quite some time doing some stuff and the stereo cut out and a few dash lights came on with the engine still running. Shut the engine down and the battery voltage was 11.90V. Not good. Battery is only a couple of days old.
Update 2: Yep two (possibly 3 but hard to see clearly) diodes in the alternator have failed with one failing catastrophically. It certainly let the smoke out.
Brushes and slip-rings look to be in good condition though.
The overrunning pulley doesn't feel correct. It locks correctly, by jamming the rotor cooling fan, but in the other direction it is hard to turn and does not feel smooth at all.
Time for a new alternator.