1. Crystallization can sometimes occur when gases go from gaseous state to solid state;
2. Crystallization can sometimes occur when liquids pass to solid state.

Both correct - as is
3. Crystallisation can occur within the solid phase as the molecular structure of the substance changes.

I would not criticise the weather site for use of the word crystallisation, for want of a better term. But it's not really the opposite of "sublimation". If the phase diagram has three single-phase regions, that gives up to three pairs of phase transitions:
-evaporation/condensation
-melting (or fusion)/freezing
-sublimation/ ?

"Crystallisation" is not really restricted enough in meaning to fill that blank.