Having managers for Gaelic football teams has not always happened. So early Gaelic Football teams did not have managers. Different people got involved in training and organising teams and doing other jobs to help out. So you could say there was a collective management for teams. So there is no real answer to your question.
GAA refers to the Gaelic Athletic Association, the governing body of Gaelic Football and Hurling, not to a sport. The GAA was founded in 1884, but its sports pre-date that by centuries. It is not known for sure when the first games of each were played, especially Hurling. There is a record of a Gaelic Football match in Meath in the year 1670, but it would not have been the first match ever. So it is impossible to say who were the first two teams to play either Gaelic Football or Hurling.
No, he is a football manager.
Sir Alex Ferguson!
Sir Alex Ferguson
Celtic's first ever manager was Willie Maley
I doubt if they had one who was both.
John Barrow was appointed manager of FC Barcelona in 1917. Barrow was the club's first ever manager. He only stayed with Barça for 4 months and never won a title with the club.
William E. Barclay was the first manager of Everton and also the first manager of Liverpool, working with club secretary John McKenna.