It'll break your frozen/cc status, yes... but in the chain-cc scenario, you'll be back frozen again after that 1 second of unstoppable has expired.
Still, better than nothing. My barbarian pre-season had two cc-break skills and still couldn't fight multiple cold-enchanted elites without being constantly frozen. Maybe a third in elixir form may have given me the edge I needed to kill them?
Yes, but I think all jobs has at least 1 skill to break CC. Either base skill or needs additional legendary aspect. Anything with unstoppable in its description. So maybe use that first