Can a priest celebrates the sacraments, particularly the Eucharist, any where or does his faculties pertain only the diocese for which he was ordained?
Within his own diocese:
Baptism is always valid.
Eucharist requires faculties for licit celebration (Can. 900 §2) but is always valid.
Confession requires faculties to be valid (Can. 966)
Marriage requires valid faculties and delegation (Canons 1108 & 1110).
Every priest validly administers the Last Rites (Can. 1003).
Confirmation requires faculties to be valid (Can. 882)
Outside his own diocese:
If a priest has faculties from his own diocese or religious order then he carries those faculties with him wherever he goes. There are only two exceptions:
to validly preside at a wedding a visiting priest needs delegation from the local pastor.
a bishop can refuse to permit a visiting priest to hear confessions thus rendering them invalid should they take place (Can. 967 §2).
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