In the case of a very difficult life question, which would involve the future of one’s entire family, is it permissible to ask Hashem for a sign as to the appropriate step to take? Some people request that one of the Lubavitcher’s Rebbe’s letters be translated; but, what of asking, for example, if the answer be yes, that a red bird appear, and if no, that a blue bird appear? Is this the same as augury, which is forbidden?

I do not think it is appropriate to ask HaShem for specific signs, and yes it can come into the category of augury. I do believe that rabbinic advise can be beneficial in difficult questions, but ultimately we go with our minds and our hearts and take responsibility for our decisions and deeds. It is certainly proper to pray for wisdom and understanding along with Divine guidance.