Most are wired through the ignition switch, so that they work only when the ignition is switched on. This prevents you accidentally leaving something switched on which might cause the battery to go flat.
Apart from the main charging, starting and ignition circuits, there are other circuits that power lights, electric motors, the sensors and gauges of electrical instruments, heating elements, magnetically operated locks, the radio and so on. All Circuits are opened and closed either by switches or by relays - remote switches operated by electromagnets.
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.
Depending on the fuse design, it is sometimes possible to tell whether it has blown by holding it up against a light; a break in the wire inside may be visible. Another clue is blackening of the glass cover. If there is no visible sign, check by fitting another fuse of the same rating; if that cures the trouble, then the fuse was to blame.