Gladly...
Thank you!
I've read somewhere (it was a Kishi interview, I'll try to find it later) that if a Hyuga and an Uchiha have a child, that child will have one Byakugan and one Sharingan. Considering Otsutsuki to be the Hyuga type (having the Byakugan), the Uchihas would most probably have Byakugan, which they don't.
No need, you're right. He said that somewhere -- But didn't he make that statement during an early part of the series? He did say he came up with Kaguya
at the last minute. Anyway, we don't know how the Uchiha Clan started up though. All they say is that it originated from the Byakugan itself.
I'll bet my money that Indra married a normal girl. Just an assumption though. This is further backed up however (below).
Listening.
Is that really the case? Because as far as I know, Kaguya was the first and only Otsutsuki on Earth who came to acquire the chakra fruit. And since she stayed on Earth from thereon, it's also highly probably that even Kaguya married a normal guy. And if it didn't affect the inheritance of genetic power, probably Indra and Ashura were the same case since they along with Hagoromo, Hamura and Kaguya were the only Otsutsuki on Earth. No other Otsutsuki came to Earth, and since Indra and Ashura lived on Earth, it's most probably that they both married a normal girl.
I believe, Kaguya ate the fruit and became the ruler of her clan (and the world) for the most part. I'm not sure if this was stated in the Manga, or her Data-Book. But I'm positive here. Considering she had the entire clan under her control, it's highly possible that she married someone in it. Though, we can't say for sure.
This depends on knowledge from above whether I am accurate as well. Because it's so-so from memory, but I'm relying on chance for this one (being a bit lazy from school, but I'm fairly certain it said she was Clan Leader).
I'm not exactly sure whether or not Hagoromo/Hamura lived in the same place, but it directly implies that in the Last. That he left Earth to go to the Moon, while his brother stayed in Earth to spread his ideology of Ninshuu. In the Manga, it doesn't imply either. We just know that they both had to bring down the Juubi/Kaguya together.
Another thing we don't know for sure is if they were all Otsutsuki, and even if they were, they did not have the special chakra that would make their genes superior.
It started from Kaguya, then Hagoromo and Hamura, then their children and so on.
Ashura and Indra as the Sage's children were the only ones who inherited his powers, which he inherited from Kaguya. So their wives would've been fodder/considered normal either way.
Hagoromo was the odd one out compared to his brother, wasn't he? He was born without the Byakugan, but had the Rinnegan. lol