The case of nivul peh that the Gemara gives is about talking about sensitive matters in an explicit and obscene way. In the words of the Gemara (Shabbos 33a):
הכל יודעין כלה למה נכנסה לחופה אלא כל המנבל פיו אפי' חותמין עליו גזר
דין של שבעים שנה לטובה הופכין עליו לרעה
All know for what purpose a bride enters the bridal canopy, yet
against whomsoever who speaks obscenely [thereof], even if a sentence
of seventy years' happiness had been sealed for him, it is reversed
This isn't simply saying 'bad words.' The rabbis taught (Pesachim 3a) that it is proper for one to speak with clean language, but dirty words are not nivul peh per se - nivul peh is something said in context.
Therefore, to answer:
1) It isn't about specific words; it is about speaking a certain way about certain things.
2) There is no indication that this issue has anything to do with chillul Hashem. I think it is common sense that this is a simple issue of character refinement, and I also posited here that that might be the biblical source for this idea.
3) Nivul peh is not classically something directed at someone.