How would rainbows appear on other planets? Are other planets capable of producing rainbows? How would those rainbows appear? Can rain, clouds or ice from elements other than water produce rainbows?

Related: https://space.stackexchange.com/questions/34357/rainbow-space-probe
Rainbows occur when sunlight shines through rain. This is rare in the solar system. Rain (of sulphuric acid) might be common enough under Venus's clouds, but there is no sun. Conversely, there is plenty of sun in Mars, but no rain, and only very rare clouds.

It rains on Titan: methane rain. Methane has a lower refractive index than water (1.27 instead of 1.33), which would make the rainbows slightly larger (though not by much 42->52). However the atmosphere of Titan is hazy, and while there is some light on the surface, the sun's disc is not visible.

There is rain in some layers of the gas giants, but again not on the outer layers where the sun is visible.

It is likely that the Earth is the only place in the solar system where rainbows are a common phenomenon.