You have normally 2 segregated electrical system (1 & 2) with, for each system, several sub-segregation (like primary, secondary, essential, secours with bus bars, contactors that can cut some non-essential systems depending on rules or switch in the overhead panel) and several sources of power (engines, apu, batteries, sometime rat).
Black boxes don’t have battery (to dangerous, the battery could destroy the recordings when damaged and that would also require specific maintenance) but normally they have several power source. Loosing power like that is strange and could indicate a fire or a maintenance problem (on board batteries should be able to work for at least 40min without engine… but they had a running engine as far as i know… that doesn’t make any sense).
APU can be run while flying, you must be below a certain flight level to use it (<FL100?).
Glorified autocorrect… YES! It’s a really good analogy that i will use to temper the expectation of my boss. Also: AI hallucination is just a fancy way to say ’it’s a wrong answer’.