Explanation #1 (Part 1): He (Elisha) ought not to have conceded to something that is an Isur, by saying 'Lech le'Shalom!' - a proof that a ben No'ach is not subject to Kidush Hash-m.

Explanation #2 (Part 2): And the Gemara answers 'One speaks in private, and one , in public' - Na'aman was in private, since there were no Jews present in Beis Rimon (when he prostrated himself together with the king).

Explanation #3 (Part 3): Whereas by Kidush Hash-m, the Torah writes "in the midst of B'nei Yisrael"; and even those who hold that 'Yehareg ve'Lo Ya'avor' applies even in private agree that this pertains specifically with regard to a Yisrael, but not to a Nochri.

Explanation #4 (Part 4): In which case, a Ben No'ach is in fact subject to Kidush Hash-m in public.

Conclusion #1: According to this conclusion, our She'eilah (whether a Nochri is subject to Kidush Hash-m or not) has not been resolved.

Implied Question: The Lashon 'Mai Havi Alah' (which introduced the current proof) suggests however, that a resolution is imminent?

Explanation #2: It therefore seems more likely to accept the text which reads 'And if he was subject to Kidush Hash-m, why did Amri beih Rav not draw a distinction between in private and in public'?

Conclusion #2: And the conclusion is in fact that a Nochri is not subject to Kidush Hash-m, based on the fact that he (Elisha) said to him S'tam 'Lech le'Shalom!'.

Implied Question: Why did the Gemara not say 'Bitah u'Bas Bitah'?

Answer: Because the Torah writes Sereifah specifically by Chamoso and bas Chamoso.

Question #1: Whereas with regard to the She'er that comes from her, the mother's mother is forbidden, with regard to the She'er that comes from him, the mother's mother is permitted?

Question #2: Moreover, according to those who hold that Sereifah is more stringent than Sekilah, whereas with regard to the She'er that comes from her, the mother receives Sereifah, with regard to the She'er that comes from him, the mother only receives Sekilah?

Answer: Since we are learning that what is written by one as if it was written by the other, one cannot ask any Pirchos.

Alternative: The Gemara in Arba Misos Darshens (from the same Pasuk) that one is only Chayav because of 'Imo', but not because of 'Eishas Av', so that in fact we learn two things from there.

Clarification: The reason that one can ask a Pircha on this Gezeirah-Shavah is because it is only 'Mufneh' (superfluous from both sides).

Question: Why can we not ask that just as his aunt is forbidden, so too is hers?

Answer: One can only ask Pirchos from Chayvei Misos Beis-Din, seeing as the Gezeirah-Shavah was said in that regard (and not from Chayvei Kareis).