I'm aware this question has probably been asked before but I'm looking to get a definitive answer about training BOs in Rank III of various skills. Is it possible to have a BO trained in skills for a profession different than you own (like Engineering III if you're a science officer) and if so how? Thanks.
Yes, as long as the BOFF is not bound to you, like the Borg Boffs or whatever.
First, commission the BOFF you want to train, so you can slot them on your ship. Then you need to find someone you TRUST, and who can train the relevant power you want trained. Then you trade that BOFF to them, they train the power, and trade it back to you. Voila!
Most people are trustworthy, but still, it is a major flaw in the system that there is zero safeguard against them running off with your BOFF. Unfortunately you can't mail a commissioned BOFF so you can't mail it to an alt to train it either, however you could have someone trade the BOFF to an alt to train and then trade back to you if finding someone who can train it is a problem.