Alternator replacement

Hello, just got this car from someone I know. They said the alternator was just replaced, the battery seems to be new and seems to hold a charge pretty well. When I charge the battery then start the car, the voltage will start out normal (14 volts). Over the course of a couple minutes, the voltage steadily drops, even if I am revving the engine, until it finally shuts off.

Okay, I have checked out the alternator and battery, both are in near perfect condition. It seems that when I turn on my lights, that is when the drain happens. Before the car was given to me, the front driver side was damaged in an incident. I disconnected all harnesses to each headlight/brights. The meter reads about 14.00 volts +/-.02. On the passenger side, when headlight is connected, it goes down to 13.30. When passenger bright is connected, goes down to 13.00. When driver headlight is connected, goes down to 12.95. When driver bright is connected, goes down to 12.80. This is all while revving the engine. Are these normal voltages? I now remember the car first shutting off on me while using the headlights. I have not connected all the harnesses at the same time yet, I just did individual.

Well, I did some more playing around and it turns out. I do not know. The alternator will go up to 14 volts, but when I idle the car, it can sometimes go down to 12.00, usually around 12.40. Is that normal for idling? This is with the lights off.

144 000 miles.

As I was driving a heard a sudden low pitch whine coming from the passenger side of the car. When I tapped the brake all power shut down for a split second and then came back on (no whining noise). When I got home I shut off the car. It had no power at all after that. I am guessing this may be the alternator. Does that sound right? Also, can an alternator that is going bad cause random weak acceleration?