Keep in mind that alternator can't or shouldn't cook the battery, for that you need an external charger.
So initial battery voltage can be higher than what it is after regular use of long enough.
No idea what you mean here but I know that the setup is correct according to the dc charger install specifications.
Alternators do fail. It was old. The mechanic who looked at it said they can fail any time. Adding the charger would have put a massive load on an older alternator so makes sense why it would cause it to fail.
It means that battery voltage is not very stable definition.
Like a rest voltage and charge voltage where before charging the voltage is lower, but higher voltage is still not charging.
Cooking means that old lead acid battery was fully loaded after few days of caps open, over a boiling point charge voltage and water added when needed.
Your intermittent problem can be anything along the route of electricity.
It also has a general and special problem situations.
General situation is that you have a situation.
Special situation is that you try to pinpoint it.
Old cars have old fixes.
One of mine was a wire between intake manifold and engine block.
The wire had a voltage, but other way was completely unknown and one spot of plastic was melted away.
That exposed spot was also intermittently shorting to block and killing something vital.
Repair was a new insulation from a cut open wire guide tube.
Pinpointing the problem can be very difficult.
If it is intermittently disconnecting spot you can possibly fix it by adding a ring source.
Means that you add a wire from the beginning to the end.
But finally, if not a wire itself, all connections are away from that ring, somewhere is a T-junction.
If it is an overloading spot you need means to record that short moment of the happening.
You also need at least one control spot where the overloading happens a bit later or not at all.
Third possibility is that you swap parts and finally have a gained trust that the problem is gone.