how can you tell if a liquid tested is polar or nonpolar?

Run it through an electric field, and see if the stream deflects.

(You can do this with water. Use the glass rod/silk trick or even just a comb that you've run through your dry hair. Run a (thin) stream of water from a faucet, then move the rod/comb close to the stream.)

Pour a known polar or non-polar liquid into the unknown liquid and see which disolves.

Doesn't necessarily have to be a solid. For the most part, an ionic solute, say table salt, is not soluble in a nonpolar solvent. The reverse also works, for the most part----Problems arise though when you have a material, like soaps, that have both polar and nonpolar components. You can sometimes discern properties of these materials, if you carefully add known polar and nonpolar solvents and observe the behavior at the boundary layer. Materials, like soaps, are called surfactants as they tend to bridge the boundary layer across immiscible liquids.

Rap

Yes, it could be a solid substance too.