Yes, a loose battery cable will prevent the alternator from charging the battery. The drain on the battery is not caused by the engine not running unless an accessory is left on. Most likely, the drain is caused by accessories (radio, lights, etc) while the engine is running due to the battery not receiving its charge from the alternator and then not having enough charge left to start the engine.
If the engine is running, then no. The alternator constantly keeps the battery charged.
Defective alternator or voltage regulator. Also possibly the battery is defective with a dead cell.
If the donor vehicle is running and has a properly functioning alternator, no.
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.
Alternator not charging battery due to a bad fusable link?
As long as you have a strong alternator you wont have any problems running your stereo.
Absolutely. If a diode shorts to ground it can drain a battery in a very short time.
Yes. If the alternator is dead and you drive the vehicle, all the power is coming from the battery and it will eventually drain completely. Also, if a diode is shorted inside the alternator, that can drain a battery.
Something is on drawing power. Can be any light on the vehicle or a relay stuck.
It doesn't actually drain the battery, but without a working alternator to recharge the battery it will only discharge as the car is operated.
A raidator in need of a flush will not cause a battery drain.