If the alternator is installed incorrectly, yes, it can drain the battery.
Probably loose drivebelt. or alternator belt of it is seperate.
There is no problem...the problem was the alternator. You have fixed the problem.
could be the alternator. could be the battery, the alternator charges the battery but does not stop the battery holding a charge.could also be a bad starter motor. take alternator off and have it tested. most places will test for free
usualy if the alternator is not defective then its the battery. you should start by cleaning the battery post. then you could check the terminal wire that runs from the battery post to the alternator. if thats not it you should check the ground on the alternator.
My advice is to charge the battery with a battery charger before starting the engine. You will be putting a heavy load on the alternator if you allow it to charge a dead battery. This could damage the alternator.
Inside the alternator
This could also be alternator problems as in a bad diode in the alternator.
Possibly a bad alternator. The Alternator charges the battery when the vehicle is running. If the battery is not being charged this could cause the vehicle not to start.
A partial earth
If the alternator is good and the battery does not charge, then the battery may be bad. There could be problem with the electronics. You will need to take it to a place where they sell batteries. They have equipment to check out the battery and the wiring.