Current flows along a single cable from the battery to the component being powered, and back to the battery through the car metal body. The body is connected to the earth terminal of the battery by a thick cable.
Some ancillary components can be operated without the ignition turned on by turning the switch to the auxiliary position. A radio is usually wired through this switch, so that it can be played with the engine off.
The current would encounter the resistance twice, and the double resistance would halve the current, so that the bulbs would glow only feebly. Connecting the bulbs in parallel means that electricity goes through each bulb only once.
The fuse box is often located in a cluster of components, as illustrated here. The box is shown with the cover off.