The OP’s first post in this thread is asking about possible damage to their car when using their car to jump start another car. The other car has a partially discharged battery presumably. Wouldn’t doing that require, for a certain amount of time anyway, the OP’s car charging the other car’s battery? Just to clarify, are you saying providing a jump start might damage the OP’s car alternator?
If you just give a basic jump start it doesn’t abuse your alternator or battery. You hook up the cables, turn the key in the other vehicle, and it fires up. In this case, your battery/alternator are just briefly giving a boost to a weak battery. You were talking about having been hooked up to a vehicle for something like 15 mins. If it takes that much, then the other battery is seriously discharged (and/or your cable connections are lousy). And for that 15 or so mins, your alternator is being overworked - supplying voltage to run your car, maintain your own battery charge, and actually acting as a charger for the other vehicle. They aren’t even designed to act as a charger for your vehicle.
And that’s the point - alternators are not designed to be battery chargers. They maintain charge on your battery, but that’s all. If you have a deeply discharged battery, then it needs to go onto an actual charger. If you manage to jump start a car with a weak battery within a couple/few minutes or less then no worries for your alternator (or battery). But for the recipient of the jump? Yes - their alternator is being abused by having to both run the car’s electrics and act as a charger.
Like I said, I don’t even install a new battery (other that in emergency) without putting it on charger first.