Is it possible to run your car's system without the engine on using a charger?

You should be fine. Just make sure to keep the voltage steady, especially when you’re programming things like BMWs. Look into power supplies designed for that purpose, as modern chargers may default to pulse charge. They typically range from 40-80 amps. You should also check your battery’s temperature during and after the movie to make sure it’s not overheating.

A used server power supply could be perfect for this. Here’s a guide to make your own: https://www.instructables.com/1200W-1224V-DC-Power-Supply-for-Cheap/

Just get some 15" Cerwin Vega home speakers. You won’t need a subwoofer with those.