mainly leaving your lights on when the engine is of or leaving the keys in the ignition
If the alternator is installed incorrectly, yes, it can drain the battery.
If the car is on (Ignition is on, engine is running) then no. Nothing should drain the battery when the car is running, there is a device called an alternator with a belt that usually goes around the crankshaft that transforms the mechanical energy into electrical energy. As long as you have the car running, the battery should not die. If so, you have a mechanical problem.
It might
You can get a car alarm that uses it's own battery so wont drain the car.
If the engine is running, then no. The alternator constantly keeps the battery charged.
If the donor vehicle is running and has a properly functioning alternator, no.
The Legacy subwoofer will really drain your battery. It's not a good idea to run it while you're not running the engine.
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.
While the car is running the alternator should be recharging the battery faster than stereo can drain it. I suspect you either have a problem with the alternator or its time to get your battery replaced. Until you get it fixed, if you don't turn on the radio, it wont drain your battery :) If it is a high power model, it needs to be wired directly to the battery.
The wrong spark plug wire(s) can cause engine problems including not running but won't drain the battery.
Either the battery has a dead cell and needs replacing or something is on pulling power from the battery.
A battery charger does one thing. It charges a battery, and starts with whatever charge is in the battery and goes from there. Running an automobile battery down will shorten it's life.