'Full age' means that she was 21 years or older. Unfortunately only the father's name and occupation will appear on a marriage certificate but both parents should be listed on a birth certificate (unless child is illegitimate).
The 1901 census for Ireland is due to come online shortly and might show Mary Jane's family if they are still in Ireland.
Where did the Power family go to in America? Each state keeps its own vital records (births, marriages, deaths) and many of them list birthdates and places as well as parents' names on death certificates.
