In Yoreh Deah 151:4, the Rama quotes the Mordechai that it is permissible to sell objects of idol worship to a non-Jew if the non-Jew can obtain objects of idol worship through other means anyway. He also quotes a few other sources that disagree, though he writes that the practice is to be lenient. The Shach (s"k 6 and quoted in Beer Heitev s"k 5) writes that even the stringent authorities quoted by the Rama agree with the Mordechai. However, the Shach there explains that to a Jew it is nevertheless forbidden; see there. However, he writes that for a mumar, he counts as a non-Jew. But also see the Dagul MeRevavah that a Jewish mumar has the law of an ordinary Jew.
This would seem to correspond to your first two cases. We would say that according to everyone, you can't give a Jew non-kosher food. However, from the Shach (not like the Dagul Merevavah), it appears that for a mumar it is permissible. What is a mumar? Does it have to be someone who worships idols, or can it even be someone who is mechalel shabbos befarhesiya (publicly)? I don't know. Although the Kitzur (72:2) writes that whoever desecrates Shabbos in public is like an oved kochavim for every matter, the Shearim Metzuyanim Bahalachah there says that this is only lechumrah; but if treating him as an oved kochavim would lead to a kula — as in your case — he counts as an ordinary Jew.
Concerning the third question, the Shu"T Teshuvos VeHanhagos (pt. 1 siman 283) writes that it is forbidden, in contradiction to the Igros Mosheh (OC pt. 3 siman 36) which he quotes there.