Mountains and solids on other planets
A planet has been theorized that forms in a primordial disk of high carbon content. See https://en.wikipedia.org/wiki/Carbon_planet. This planet's crust would have a high hydrocarbon content and thus not be very "solid". However, such a planet might theoretically have volcanoes that erupt diamonds, so an alien could build there home out of diamond!

Another hypothetical planet is a waterworld or ocean planet. If there is indigenous life then the only "above water surface" would be composed of life (ie: mats of algae type material floating on the sea).

As far as mountains go, this is not a question of solid or not solid. A large superearth would likely not have much in the way of mountains because of the high gravity at the surface. It might be noted that with out plate tectonics, we wouldn't have mountains and the Earth could arguably be covered in a global ocean.