My cousin has chickenpox and I came in contact with him. How contagious is it?

Very contagious. Chicken pox (varicella) is very contagious. If you previously were vaccinated or have had the disease, your chances of getting it are very low. If you have not had the disease or the vaccine, and you were just exposed, you potentially can get vaccinated to try to help protect you. Contact your physician. You can also call the cdc hotline at 1800 232 2522 and ask for advice for free.
Very. But it is likely that you have been vaccinated to protect you. Which means you won't get it. But in the case you didn't receive the vaccine then it may be up to 21 days before you show symptoms.
Very. Spending as little as a half hour in the same room is enough to infect a vulnerable person. Most adults are immune, even if they don't remember having it. If you know for sure you didn't, the vaccine can help if you get it immediately. It can be horrible on adults. The incubation is 10-21 days. If you start to have symptoms call your doc for antiviral meds.