Hi Allendc,
I don't have my books in front of me......but..
Doesn't the APU use AC power to start when it's available, and if it's not available, ie. cold start, then the main battery charger wouldn't be powered to do anything!
The third item, the standby power in auto etc, then as you say, transfer bus 1 is not powered therefore how can the battery charger get power, unless external power is connected.
I agree with the last item.
But without my books, or a good Flight Engineer, I don't know about the rest!
Cheers, FD