1. Kaguya gave birth to Hagoromo and Hamura after eating the Shinju's fruit. I highly doubt a goddess like her would have produced offspring with some random fodder. Of course, her husband has to be a similar level god.
2. I presume both Momoshiki and Kaguya ate the Shinju's fruit together (half), which granted both of them special powers. Rinne Sharingan on Kaguya's forehead and Rinnegan on Momoshiki's palms. This also explains why he wants Naruto's Kyuubi, he wants to reincarnate the Juubi i.e. reincarnate Kaguya or just merge her powers with his own powers for something even bigger i.e. the original chakra monster.
3. Hagoromo must have inherited the Rinnegan from this guy. It's said that Rinnegan is derived from the Rinne Sharingan and Hagoromo inherited Rinnegan from that but I think it's a purposely made up assumption, because it honestly doesn't make sense. If Rinnegan is a derivation from the Rinne Sharingan, then what's stopping Kaguya from using the powers of the Rinnegan from her Rinne Sharingan? Why are her powers only Sharingan related? It's presumable that Rinne Sharingan is the progenitor of Sharingan only since it looks exactly like the Sharingan only and possesses only Sharingan related powers to the utmost level.
4. The other half of the Shinju's fruit's power (presumably eaten by Momoshiki) must have manifested the Rinnegan in Momoshiki's palms (an illogical but most sensible secondary place for two additional eyes) just like Rinne Sharingan manifested on Kaguya's forehead (an illogical but most sensible secondary place for one additional eye). Momoshiki must also have some Juubi like transformation similar to Kaguya with two Rinnegans instead of one Rinne Sharingan.
