What properties a compound should have to be called an "ice"?
Ice is a term usually given to $\ce{H2O}$ in the solid state. Solid carbon dioxide, what is sometimes called "dry ice" is actually a misnomer — although the gas is frozen, it is not truly ice, in the chemical sense. It is called dry ice because instead of melting into liquid carbon dioxide (like actual ice, which is frozen water to liquid water), dry ice sublimates into it's gaseous state, skipping the liquid phase (almost — still goes through liquid phase, but this happens so fast it's basically negligible) entirely.

As for properties, you basically have all of them listed.