1. Hingashi and Doma are both Japanese inspired. The Steppe is indeed based on Mongolia.

2. Geisha / courtesans are prominent in both societies; Kugane has an entire red light district (Sanjo Hanamachi) while Yotsuyu was known to have been... owned by a Doman brothel. Hildibrand shows up in one of his 4.x quests, and while people are surprised it's not because he's male at all, but because they hadn't requested a male.

3. Other than Sadu apparently practicing what we know as Thaumaturgy, the East seems to have its own magical traditions. They are probably similar to the Eorzeans' in practice, but with a different history behind it.

4. Not sure... I'd need to comb Kugane for people with both a first and last name, I suppose.