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Oh ho ke na ki?

It is modern Japanese pronunciation. In classical literature, おほ is pronounced as a prolonged "o" (an elongated /oː/ sound).

Does that apply to longer vowels with the same(ish) sound, as in 因果応報?

Yes, and no. 報 . this is contemporary word. it pronounces "ho-o", not "ho", not "o-o", not "o". Someone read "bo-o".