Re: Mouthpiece breathing..
Well, if you're gonna train with a mouthepiece, then the obvious answer is yes - inhale and exhale through the nose. That's the whole idea.
Personally, I can appreciate the logic behind doing this, and if you can do it - all the power to you. Your conditioning will be superb.
But training with such a handicap (obstructed breathing) could also make your conditioning sessions miserable, and you may have trouble keeping up with training partners. If you become de-motivated to train because it's too punishing - that's counter-productive in my opinion. As I speak, i'm sure people have done this before with success, so i'm not saying it's an outright bad idea.
I'm simply saying, you can add as many handicaps to your training as you like to get the most out of it, but as individuals, we need to maintain a healthy balance of fun and goals that are realistic and achievable.
Good luck with your training. I'm eager to hear how this works out.