When doing Deep Meditation and intoning the mantra, should one breathe in and out through the nose or mouth?
I am aware that in general it is much healthier to engage in nose breathing but I know different types of meditation have their nuances and it doesn't seem to be specified in the DM book.
Yes, breathe through the nose whenever possible. If you can't breathe through the nose because it is blocked, then breathing through the mouth is fine.