The nice thing about Gregorian Chant is that the "Do" is movable. So you sing the melody where ever is comfortable to the singers you have available to you. The C Clef (Do) or the F clef (Fa) are there so you know where the "Do" or "Fa" is on the staff. I hope this helps. Keys are for the most part irrelevant.

It's most pure form, Gregorian Chant is sung in true unison, not in octaves.

However, if you have a mixed choir or are singing it congregationally, there's no particular rule stopping you from singing it in octaves.
(An alternative to that would be singing it antiphonally, a phrase at a time back and forth between high and low voices, of ten with the very last line sung together in octaves).

For congregational chant, I generally have everyone sing everything.

For chant with my choir, I only do mixed octaves for short bits- the last phrase of a piece, the Amen, an Antiphon, etc- I always switch back and forth between men and women, either line-by-line or stanza-by-stanza.

I, personally, would never have a single-gender (adult voices, I mean) group sing in parallel octaves. It makes no sense to my ears. When I have had low-voiced women, they sing with the men. I've never had a male singer with a voice so low that whole group couldn't find a suitable middle-range pitch.

What do you mean "which octave?" They've transposed it slightly, and go from the D below mid C, to the D just above mid C. (Sorry I can never keep track of D vs. d vs. d1, etc.)

to melocharles' point....

What I said above is my OPINION and PREFERENCE based on my own MUSICAL TASTES.

While the music of chant is in service to the word (as opposed to the music itself being the point), it should still be sung "as music" and one's own artistic sensibilities should be considered. Questions of accompaniment (whether and what kind), voicing (mono-, mixed, organum), rhythmic interpretation (Old Solesmes, semiology), and so forth are not (IMHO) matters soley of academic/historical interest (and correctness) but rather represent a wide variety of legitimate performance practice which each LITURGICAL ARTISAN will draw from in producing a performance (for lack of a better word) which is beautiful and relevant in the context of their own community's tastes, preferences, and resources.

In other words...
learn as much as you can about what other people are doing or have done, steep yourself as much as possible in the tradition, and then go and do what makes the most sense to you. It's a living tradition and a vital artform. It is not museum curation.

The choir I direct at a large suburban parish only sings chant in one octave. I've found that both the men and women are better able to stay in key if they don't have the octave above or below them in their ear. Therefore each week the women sing either the Introit or Communio and the men sing the other. This also cuts in half the amount of chant they have to learn.