"May we always praise the God and Father of our Lord Jesus Christ". This refers to God the Father. It is best to translate "Father" with the same word that your language uses to refer to a human father.
Both phrases refer to God. Possible meanings are 1) that the words "mercies" and "all comfort" describe the character of "Father" and "God" or 2) that the words "Father" and "God" refer to one who is the source of "mercies" and "all comfort."