I have a handle but no hands, and a belly full of other lands. Though I travel far and wide, I always stay by your side. What am I?

The process starts with a wheel spinning fast, Onto it, a wet blobby lump is cast. As fingertips shape it and sharp edges loom, Without me, it never escapes muddy doom.

A creature so rare, with a horn like a crown, it prances with flair. In dreams, it's found, with grace and charm, a horse-like wonder, causing no harm.

What is something you can catch but never throw?

A raindrop falls, a circle grows, across the water’s face it goes. Though I am neither fish nor wave, what am I that outwardly strays?