Each of the four sections would possess it's own bridge, engineering, life support, medical and weapons
But the Prometheus
sections apparently didn't. Only one sickbay was used and implied, and there was no crew in the sections that separated to fight the Bonchune
Indeed, the big plus of a separating ship would be that her various components can be maintained and repaired by crew during combined flight, but can fight without risking any lives during separated flight.
Just sending out droneships from Starbase 123 would mean that they may suffer engine breakdowns en route, or may arrive with outdated intelligence and can't think smartly enough to adapt to the new circumstances. But sending these drones aboard a crewed carrier eliminates those problems - and making the drones larger than the carrier is a sensible move, because big drones with big engines and big guns are likelier to score victories.
And yeah, gravity should be freely adjustable, in direction as well as strength: we have seen that side-by-side rooms can have different gravity settings... If anything from one gee to zero gee is possible, why not from zero gee to minus one gee, too?