Either the battery has a dead cell and needs replacing or something is on pulling power from the battery.
If the alternator is installed incorrectly, yes, it can drain the battery.
mainly leaving your lights on when the engine is of or leaving the keys in the ignition
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...
only if the car your using to charge the other on is not started