Damage and repairs
Damage stays until someone fixes it. Engineers and the right buildings do the fixing.
After a fight, damaged buildings slowly repair themselves, and much faster with engineers at the base. Repairs cost a little money as they go, and stop when your War Budget is empty.
Damaged units do not heal on their own. Rest them at one of your bases with the building that makes them: a Barracks for infantry, a War Factory for vehicles, a Shipyard for ships, an Airfield for aircraft.
Engineering Squads fix army vehicles in the field: in their own group, or in any group they can reach. More engineers fix more vehicles at once.
Nothing is repaired during a battle or on the move. A destroyed building is gone for good, freeing its slot for something new.