Is chicken pox contagious?

Of course it is. Of course thru droplets, respiratory and contact. Immunization provides protection. It is safe when ther are no new lesions and all the old ones are scabbed over.
Very! Spread by droplets from mouth or nose (like coughs, sneezes, or breathing) or from contact with clothes or other items contaminated by skin sores. Very easily spreads. Contagious for up to 5 days (usually just 1-2 days) before the rash breaks out until about 5 days after. Once all pox sores are crusted, contagious period is over.
Yes. This is a highly contagious disease in nonvaccinated individuals.