Yes, the voltage increase to such a limit is acceptable, but if you observe such phenomena and it will certainly happen, you need to lower the voltage, which will limit the current or simply limit the current. And as for disconnecting the battery while the engine is running, agree, of course it is unhealthy. Theoretically, the voltage regulator should maintain the voltage, but this is just a theory and without the battery load, it will increase and most often cause damage. I had such a case in an old Fiat, the battery died completely and the cables were gone, the old type of mechanical regulator, I started the car to quickly replace the battery with a charged nap. It shocked me quite well when I touched the terminals without the battery to such an extent that I could not tear myself away. What the tension must have been, it must have been considerable.
Many a weaker rectifier without load gives almost 20V and this drops under battery load.
As for the internal resistence, it depends on your look, you look at it as a source, and I look at it as a receiver in the charging circuit, and because it is also a source, it gets interesting. And my colleagues see that one could write a book on this subject without exhausting the topic. I'm trying to coat it over here.
Browse the net, I found one more interesting theoretical material
http://www.zkue.ime.pw.edu.pl/~jarek/Diagnostyka/INSTALAC/Instalacja.pdf And interesting experiments with us
https://www.elektroda.pl/rtvforum/topic396537-0.html SławeK