How and when did St. Gabriel die?
St. Gabriel is an archangel and will never die. However, if you are referring to Saint Gabriel Possenti, he died on February 27, 1862, at Abruzzi, Italy of tuberculosis.
The Catholic Church, and other churches, have traditionally honored the angel Gabriel with sainthood, and there is consequently a Feast of St Gabriel, which was added to the General Roman Calendar in 1921. Various churches are called St Gabriel's Church. Given that Gabriel was an angel, not a human, and that Gabriel is always mentioned as serving faithfully as one of God's angelic messengers, there is no reason to believe that Gabriel has died.