Do other planets have shooting stars?
Yes. Any planet or moon with air can have shooting stars. Mars, Venus and the giant planets all get them.
Shooting stars happen whenever a speck of space dust rushes into a layer of air and heats it until it glows. So any world with an atmosphere can have them.
Mars has a thin atmosphere made mostly of carbon dioxide, and space dust hits it all the time. Scientists think a camera on one of the Mars rovers may have caught a meteor in a photograph in 2004. Spacecraft orbiting Mars have also seen signs of space dust adding metal atoms to its upper air, just as happens on Earth.
Venus has a very thick atmosphere, so space rocks burn up or break apart high above its surface. The giant planets Jupiter and Saturn have deep atmospheres of hydrogen and helium. Jupiter, with its strong gravity, gets hit a lot. Amateur astronomers with telescopes have filmed bright flashes on Jupiter several times since 2010, made by objects perhaps a few metres to tens of metres across exploding in its clouds.
On the Moon, which has no air, there are no shooting stars. Instead, space rocks hit the ground directly, sometimes making small flashes of light that telescopes on Earth can see. Each world has its own kind of space-rock show.