Does the high pressure power steering line leak - if so the alternator is chock full of power steering oil and its eaten away the brushes and copper slip rings on the alternator and now its ****ed.
Get a cheap multimeter, put it on 20V DC,
Start the car,
Put the probes on the positive and negative terminals on the battery, you're looking for 13.8-14.
4V,
Then turn on all your electrical accessories - the headlights,
HVAC fan on full, AC, wipers, stereo, and see what the voltage does.
If it starts dropping, and it goes down to sub 13V, then the alternator is cactus and its not holding up under load and needs to be replaced.
If it comes off looking like it come from the titanic, the power steering line is leaking into the alternator, you MUST replace it with a new one before doing the alternator, or 6 months later you'll be buying a new alternator again.