Theory of an alternator.
To control the voltage the alternator turns of and on very very fast, this is called pulse width modulation. Wiki it for more background.
This means that the voltage spikes very very high for an instant and drops to almost zero before it turn on again. To keep working, and it will try, it burns itself out by going to to high a voltage to often.
I've have never heard of an Is400, but if it is wired correctly it should have a fuse.
I've never seen a pump on any alternator.
If the battery is sulfated (or otherwise faulty) to such an extent that it calls for a continuous charge, the alternator never gets a chance to switch off. With the resposibilitiy to run continuously the alternator overheats and eventually fails. Never replace a faulty alternator without also checking the battery.
That is the purpose of an alternator. The keep the battery charged and to run all the electrics on the vehicle. However it is never a good idea to allow the alternator to charge a dead battery. This will put a strain on the alternator and may damage it.
It checks many things, connections, belt, and voltage regulator. I have never checked one with a load test. On a modern car or truck, never ever disconnect the battery from the alternator with the motor running to check the alternator. It can burnup a lot of electronics instantly.
I assume you mean how long to charge the battery. You should never let the alternator charge a dead battery if possible. The alternator is designed to keep the battery charged but not to charge a dead battery. You put a strain on the alternator and it can cause a diode to burn out. Drive home and then put a battery charger on the battery to fully charge it.
just the belt, should never cost more than 100 dollars. It is only a 10 or 20 dollar belt and the work to install it at most should take 30 minutes.
Replace the alternator. It sounds like a defective regulator, and it is located inside of the alternator. The volts should never go any higher than 16.
Take it to the shop if you have never done it before
Most alternator brackets will have moveable bushings (short sections of pipe usually with a slot in them, in one of the engines brackets) that pinch onto the alternators mounting lugs tightly even after the bolts are removed, you should be able to pry the alternator free, tapping on the engines brackets (next to bushing not the bushing its self) may aid removal, be carefull some are cast aluminum and are breakable.
no There should never be an apostrophe in "never".
Recharging a dead battery by using jumper cables connected to another vehicle is a very bad idea. You are overworking the alternator on the donor vehicle and can very well destroy that alternator. Recharge a dead battery with a battery charger and never with another vehicle.