Yes,but... Since the vaccine has been routinely given starting in the 1990's, the number of people who have immunity because of previous unknown infection has seriously decreased. Thus it depends upon your age. If your were born prior to introduction of the vaccine, you may be immune, but do not count on it. Best choice is to immunize for safe protection!
Maybe. Most of us have immunity from chicken pox because we had it as a child. If you have not had it as a child or cannot remember, your doctor can check a blood test to find out if you have already developed immunity. If you have not, and are not pregnant, you can get vaccinated. Chicken pox as an adult can be deadly and while pregnant can be devastating for the baby.
Maybe. Most adults (>90%) have blood test evidence of prior CPX & immunity even when they don't remember having the disease. You can have the blood test run, or get the vaccine if done ( with some benefit if done within 48-72 hrs of exposure). If not, the incubation is 10-21 days & it can be hard on adults. Your doc can give you helpful meds if you get it.