If your electrical system is working as it should, using your headlights will not drain the battery. Of course that is assuming your engine is running. More than likely your alternator is not putting out enough voltage to keep the battery charged with the headlights on. Take your car to a trusted mechanic or auto parts store and have your charging system checked. You may need a new alternator. A loose drive belt can also cause this so make sure the belt is in good working order and adjusted correctly.
The new alternator is bad happens all the time.
Battery drain would depend on what else is on, for example headlights, courtesy lights, glove box light etcetra. If there is nothing electrical on then there should be no drain.
leaving your lights on for a long period of time.. headlights or just playing the radio and leaving it play for a long time
Yes, if the relay was stuck it would drain the battery.
No. The power to illuminate the Daytime Running Lights (DRL's) is supplied by the alternator, and does not have to be supplied by the battery. Once a vehicle is started and the engine is running you could remove the battery from the car entirely and everything requiring current would still operate.
Yes
Because if you reversed the polarity at the battery it would blow the fuse through which current flows to the drain.
Its not charging.
A car battery in any car would drain due to a short in the electrical system.
A bad battery or faulty battery connection.
Headlights run off the battery not the ignition...
A broken wire, a dead battery.