1. In the original cases, the second one (Conservative conversion including milah), it might be a shailoh if it was valid? Would you use the person as a Shabbos goy or to buy your Hametz on Pesach? If the person is Shomer Mitzvah (as we understand it), it would be a shailoh.
2. Referring to Middle Eastern Jews (including Yemenites, Iranians, etc.) as “Sefardim” is a misnomer (just as referring to people who hate Jews as anti-semites is a misnomer). Their siddurim say “Sefardim v’Edot ha-Mizrach”, since the nusach of the Middle Eastern Jews (excluding those from Arabia) is closely related (study migration patterns to see why). Someone suggested using the term “Afro-Asian Jews” which is technically more correct but sounds too funky.
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