1)
Is there a connection between Na'aman knowing that Elokim is only in Yisrael, and taking his gift?
1.
Malbim: One may not take a gift from a Nochri on the day of his festival, lest he go thank his idolatry [that his gift was accepted]. All the more so this applies now that Na'aman was ecstatic over his cure! Therefore, he said that he now denies idolatry.
2)
What is "Brachah"?
1.
Rashi: It is a gift of Shalom that a Talmid or servant gives upon seeing his Rebbi or master. Radak - this is like "Kach Na Es Birkasi" (Bereishis 33:11).