Diode voltage drop

No... that would be the internal resistance of the power supply.

The drill charging resistance, if it were using 800mA while at 12V, would be 12/0.8 = 15 ohms

Yes of course you are correct. Actually that's what I meant but I misstated it. Thanks for the correction.

Of course, all this is an extreme oversimplification...

Yes, maybe so, but that's probably appropriate for this thread.