It depends where the short occurs.
You have a short circuit in your wiring. You need to take your vehicle to a mechanic to have it fixed before you damage your battery.
a short in you wiring harness
There are a number of reasons why your wipers may come on by itself when driving. You may have a short in the wiring.
A constantly 'blowing' fuse is an indication that there is a short circuit somewhere in the wiper motor wiring. Or the person driving it
Bad wiring can cause a short in the radio. Bad battery will not.
Certainly could, especially if the bare wires that were connected to the lighter mechanism short out (touch) together. This will cause a dead short and render the car's entire electrical system inoperable.
You have a short in the wiring, find the short and replace the wire. Tip: The vehicle is 60 years old, I would replace all the wiring, they may have complete wire harnesses for that vehicle. (J C Whitney's maybe).
If the reverse light on a Citroën C3 stays on while driving, it may be due to a malfunctioning reverse light switch, which is typically located on the transmission. This switch may be stuck in the "on" position or have a wiring issue. Additionally, a short circuit in the electrical system could cause the reverse lights to remain illuminated. It's advisable to have the vehicle inspected by a mechanic to diagnose and resolve the issue.
If reverse lights remain on while driving, it could indicate a malfunction in the vehicle's neutral safety switch or reverse light switch, which may be stuck in the "on" position. Additionally, issues with the wiring or a short circuit could cause the lights to stay illuminated. It's essential to check these components to ensure proper function and safety. Seeking professional assistance is recommended if the issue persists.
A short circuit either in your wiring system or electrical panel could cause your fuses to blow. Most likely, it would be caused by a burned out wire which is frayed and touching a piece of metal in your vehicle.
bad switch or relay, possible short in wiring
It is possible to have a short in the wiring harness to the battery. If there is a lot of corrosion where the cables connect to the battery, this may be and indicator. That is only one possibility.