Would using the cigarette lighter socket to charge a phone while using the sound system to watch TV/movie drain the battery?
Yes of course it will .
The key detail–which the OP omitted–is whether his engine was running while charging the phone and watching a video.
If the engine was running, it shouldn’t be a problem, as long as his alternator is healthy.
If this was done with the engine off, then–yes–it will drain the battery.
Eventually, yes. When power was interrupted due to a storm I would charge my phone in my truck, battery had enough capacity to charge the 2200 mah phone without problem. But more phone charging without recharging the truck’s battery would eventually drain it.
Depending on how old your battery is.
Your “sound system” draws 10 times more current than your telephone.
That little battery in your phone cannot draw all of the energy out of a 40 pound lead acid battery.
Doubtful charging a cell phone would do it, but running the stereo-entertainment electronics definitely could. especially w/ tv-type screen, or the sound was pretty loud.