big wig = VIP (a very important person)
Yes - but usually within a particular sphere. So - someone may be a bigwig Hollywood producer wielding a lot of power and influence, yet outside the industry, few people would know his name.
hang in there : more, to remain persistent and determined in difficult circumstances - to keep going despite how hard the going is.
be at complete loss = be puzzled, be bewildered, be perplexed
Yes - mystified to the extent that the person doesn't know what to think, say, or do.