Breathing in and out of alternate nostrils is a method used in pranayama to control the nervous system using breath. Usually it’s used to put a person in a particular mental state which is conductive to meditation. To put it in a more scientifically it is used to change the brain waves from beta to alpha and frequencies below alpha. When I sink my weight I usually find myself exhaling but when I raise my weight or jump I usually inhale, just feels natural for me but I guess others do different. As for slipping and shuffling I think I mostly exhale but not always. I have not yet resolved in my mind if it’s best to inhale or exhale when taking a punch. I think there are two different schools of thought on this. One is to resist the impact by forcefully exhaling and the other is to absorb the energy by inhaling. When inhaling it will force the diaphragm down which will compact the abdomen, if this is done at the same time as tensing the abs it seems the logical approach to withstand an impact. Strangely enough my teacher says you should not tense but relax when taking a strike but it dose not seem logical to me to do that.