So when I was playing a working week, I had to alt-tab in/out of the game to check a thing after some of my hoods were arrested after gunning down an enemy gang member who attacked first.(I even got the combat notification first before the seeing an enemy gang member message.)

Next-Week, while they were reported as arrested, I can still give orders to them on the planning thing and they're not arrested unlike another hood who was arrested earlier for being wanted.

While I've yet to start the next working week, does this mean Self-defense is possibly and hoods will be let off if the other member attacked first in sight of the cops?

hmm i dont think this is the case, however sometimes the police will go after the first shooter , and if your hoods dont have anyone else to shoot and it was only one gang member that attacked them, then i think they might get away with it due to the police AI , best thing to do is not arm any of your grunts that run the doors, only the ones who are guarding office / high buisness