We've been here before, "giving thanks". Gratitude is pretty central to the spiritual life no matter what your belief system is, so it bears repeating. Giving thanks. Present participle. Ongoing.
"to God the father": this image of God has permeated much of Christian thought, but we must remember it is just an image, just one image of who God is. Play with some others and see how they feel, how they fit, how they stunt or deepen your relationship with the Divine.
In this context, the author seems to suggest that the important image is less the name than the meaning, that God, whatever we call the Divine, is the source of all for which we give thanks.