Sounds like a plan.
One thing that is really helpful to understanding the parts, is the relation between electricity and magnetism.
Basically, if a wire is formed into a circle and electricty passed through it, a magnetic field is created.
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Wrap it enough times and the magnetism is strong enough to move things.
It works the other way too.
If a magnetic field is spun passed coils of wire, electricity will flow in the wire as long as the two ends are connected to something, like a light bulb.
The wire windings in the rotor create an magnetic field when electricity flows through it. Spinning that magnetic field induces electricity to flow in the surrounding wires that don't move. The faster the rotor is spun the more electricity can be induced in those static wires. That's how the alternator can use just a little current (no more than 3 amps) to create a lot more.
Sometimes its helpful to look at the earlier system because its wiring is simpler.
When voltage drops, electricity is permitted to flow through directly the regulator.
When voltage starts to get too high, no electricity flows through.
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When electic current is allowed through the regulator it goes to the positive field terminal, then through the carbon brush that rubs against the spinning copper ring.
That ring is soldered to one end of the windings.
The other ring is soldered to the other end.
Probably not, but if a diode can fail, a stator winding can have broken connection, and the output terminal could have been not snugged up, etc. In Feb I returned AC Delco GM type alternator because the output terminal wasn't snugged up - nor could it be. One new but junk part was all it took for that alternator to 'go bad' in less than 500 miles.
Hard to draw a conclusion with a bad battery connected. See what happens with the new battery. Without a ammeter, cant say for sure whether the battery is charging or not.
hate to say, but going below 12 Volts during start is not that unusual. IIRC one of the shop manuals I have mentions using voltage during start as a crude test. Above 11 would be OK. Now if the Mallory needs I can't speak to.