Re: Alternator or voltage regulator?
Cranking with a low battery causes the starter to draw excessive current, the armature isn't breaking connection fast enough. Death to a starter eventually. (You'd think it draws less current with lower voltage according to Ohm's law, but remember the commutator interrupts the current, so the interruption isn't as fast. Each segment has a chance to overheat.)
The alternator regulator tests -
If it's got an external regulator - disconnect the field wire at the alternator. Temporarily touch a jumper lead to the alternator's field terminal, the other end to (+) battery. If it charges, alternator's OK, regulator or wiring is bad.
If it's an internally regulated alternator - look on the back for a hole about 5/16" diameter shaped like the letter "D."
Insert a small metal object, like an Allen wrench or short pocket screwdriver into the hole while running (if you have the right hole there aren't any rotating parts to hit - be sure it's the "D".) Reach in abot 1/2" till you feel something, then angle the Allen wrench so it grounds to the case. If it charges then, regulator's dust, alternator's OK. You are bypassing the regulator just like you did above.