In confession, who is being addressed, God or the priest with, "Forgive me, Father" or "Bless me, Father"? Also, when discussing a priest, would you write "the Father" with a capital F, as opposed to "the father" as we would write "the president"?
In the sacrament of confession, when the penitent says "Bless me, Father, for I have sinned," the penitent is talking to the priest. The priest in the sacrament of confession is acting in the person of Jesus Christ (in persona christi). When the priest absolves the penitent, he doesn't say, "God absolves you from your sins" but rather "I absolve you from your sins," because he is acting in the person of Christ at that moment.
Only God forgives sins. Since he is the Son of God, Jesus says of himself, "The Son of man has authority on earth to forgive sins" and exercises this divine power: "Your sins are forgiven." Further, by virtue of his divine authority he gives this power to men to exercise in his name (Catechism, 1441).
When writing about a priest, unless you are using the word father as a title (e.g., Father McKenzie), you would lowercase the word. But it would probably be better simply to use the word priest.