the construction of a question depends on who are you asking 몇 살이야? - when asking a kid or a person way younger than you / lower by social status 몇 살이에요? - children, not so young, but still younger than you 나이가 어떻게 돼요? - for someone of your age or status or a bit younger/lower 연세가 어떻게 되세요? - when asking senior person (older or higher) be cautious when talking or asking to seniors or strangers ;)

I can't help you out for most of this question, but yes there is a Korean age. When you are born you are 1 years old (they include the time when you are in your mom even though its 8 months). Then everyone ages up on the same day. the new year. So to find out your age take this year minus the year you were born then add 1. I hope that helped.