it can be caused by a bad alternator
If your battery is not fully functioning and needs to be replaced, it can make the alternator work harder. This could cause a brand new alternator to go bad. Check your battery, if the battery is not the issue, return the alternator, it should have a warranty on it for at least the first 30 days.
No, it will not.
You cannot predict when an alternator will go bad. It may last 150,000 miles and it may only last 50,000 miles. It may go bad due to a bad bearing or internal short.
The alternator is belt driven and so is the water pump but that is where the correlation ends. There is no way a bad alternator could cause a water pump to go bad unless the alternator pulley was warped. Then there is a small chance.
If bearings go bad they will "squeal"
Yes it could.
A bad alternator will cause a battery to go bad. It does not have an effect on the air conditioner.
No not necasairly
You would probably toast the diodes in the alternator.
A bad belt, a bad regulator in the alternator or bad brushes in the alternator.
If bearings go bad on a alternator/ will make a grindind noise or long squilling noise.. but if only electronic's inside alternator are damage no noise wil be heard