Feivel, the point is that iti s questionable if shaking hands in a business situation is derech hibba v’taava or simply a formality. Rav Herschel Shachter and Rav Aharon Solveichik permitted it – and Rav Yaakov Kaminetzky said in Emmet l’Yaakov on Tur Shulchan Aruch p. 405 note 4 “Regarding returning a handshake to women when they extend their hand first in greeting, not in an affectionate manner, this is a very serious question and it is difficult to be lenient. However, in circumstances where the woman may come to be embarrassed, perhaps one could consider being lenient. This requires further study”. Rav Moshe himself (Iggerot Moshe EH 1:56 at the end) that there are yirei Hashem who shaker hands when women initiate it and suggested that they hold that it is not derech hibba v’taava although he said that it is “difficult” to rely on this.
On the hand, there are issues of embarrassing someone,causing hatred, losing a job or job possibility. These all might be good reasons to rely on lenient opinions.
As for your smart-aleck examples, what is wrong with eating in a gentile home per se? If they offer you unopened certified kosher cold cuts on paper plates with plastic knives and forks and cold drinks in paper cups (although really if their utensils are cold it is not a problem b’diavad) it is totally permitted. The other examples do not deserve a response.