alternantor keeps killing battery and cooling fan wont cut off unless terminal

What is your question?

I have a 1997 accord and it had a problem with starting up and i was told it was the alternantor not charghing the battery. so i bought a new one about a week ago and had it installed. I didnt drive the car because it still had a heating problem that i recently corrected.so i took it out fir a spin yesterday and it was fine untill i went out latter in the night and came back to a car that wouldnt start. Now Im being told that the alternantor is the problem again how can this be and its a brand new 1. Could it be that even after i turn off the engine the cooling fan still runs. i need sum serious help imma single mom n tryna get this dun on my own. What else cud be wrong. there seems to be alot of wires bout the place