1. The Pri Megodim holds that there are 2 possible meanings to “omain”: A. The meaning of “belief.” With this meaning, “omain” implies that “I believe that this is true” — after praising a virtue of Hashem. B. The meaning of “fruition,” (“sheye’amen — that it come true”) — which is a prayer that what is requested should be granted by Hashem. Therefore, after someone says a blessing which includes both of these ideas, the Pri Megodim holds that we should say “omain” twice, one for each meaning (even though it is usually forbidden to say omain twice). An example of this phenomenon is the bracha in Shemoneh Esreh, “Refa’einu — Heal Us” — a request, which concludes with praise, “Rofeh chol basar — He who heals all flesh.”
2. (1:) Al Biur Chometz. (2:) Lehadlik Ner Shel Yom Hakipurim. (3:) Menachem Tziyon Uboneh Yerushalayim. (4:) Birches Ha’ilanos.
3. (1:) If one circumcises himself, he says the blessing: “who sanctified us with His commandments, and commanded us to enter the covenant of Avrohom Avinu.”
4. Borei Me’orei Ha’eish is only recited on motzoai Shabbos and motzoai Yom Kippur, and Yom Kippur never falls out on a Sunday or Tuesday.
5. Birchas Hachama.