No doubt you are just fine. Nice work on all that other stuff "while you were in there."

Does anyone have any theories about how using a new alternator to charge a weak battery could "risk limiting the life of the alternator." The only one I can think of is that if you try it on a dead battery and it won't charge because the battery is dead, and the owner incorrectly thinks the alternator is bad, and takes it back to the store, yes that would limit the life of the alternator. But other than that ... ???

Also, whenever you measure voltage, especially in these cars, it does matter where you measure it. Measuring at the battery jump ports in the engine bay should equal V at the battery posts. But that voltage will be higher than any system voltage read off a wire, or by the computer or any gauge you may have installed. Usually I think about 0.3-0.4V lower on the BMW displayed voltage vs. the jump ports. And that's for battery (engine off) or alternator (engine on).

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2001 X5 3.0i, 203k miles, AT, owned since 2014