Great thread!
1. The Khanid bloodline were willing volunteers to join the original reclaiming on Athra. Joined willingly, became well-known ground soldiers, and cemented their place in the racial pecking order by helping the True-Amarr conquer Athra. After the Empire gained space, the true-Amarr heir and leader of the Khanid people were given/earned those systems that currently make up the Kingdom. Much like the Tash-Murkon or Kor-Azor regions.
2. Udorians - from what I can tell the distinction only matters to those nobles that are paying attention. IE many true-amarr are always going to look down their noses at any Tash-Murkons (for being Udorian, or for buying their way to Heir status).
3. We'd all do well to remember just how crushingly all-encompassing and strict the social hierarchy is in the Empire. It generally takes decades/centuries for a family to move a few rungs up the ladder relative to their peers. There are only a few 'fast track' methods to advance.
The Imperial Navy seems to be one of the only institutions that allows some non-racial advancement up the ranks. I'd still imagine this to be -extremely- slow advancement. Perhaps your great grandfather was an ensign, did his job well, and perhaps your grandfather got to move up a single rank due to that reputation, etc. I have to imagine the ni-kunni's of high rank have had family members bearing the torch for many, many generations to get to those positions. It's nothing remotely like the State or Federation where you could be rewarded and quickly rise based on things like performance.
Merchants/Money: Tash-Murkons show that with enough time, money, and shrewd maneuvering that one can buy/bribe/marry their way to the top regardless of racial limitations. I'd like to imagine after Khanid II left, with the chaos at a good chunk of the military suddenly gone and a disastrous effort to take his lands back, that Tash-Murkon donated / wrote some rather large checks to re-fund the navy and get defenses back in order.
Capsuleers? I think the jury is still out. I feel like with regards to any nobility or houses the capsuleers would probably be looked upon as great champions or figureheads, but would be kept under extremely tight leashes. IE I don't see any ni-kunni capsuleers making a fortune on the market and buying themselves into heir status anytime soon. BUT I could see them buying themselves some minor titles/holdings and starting the ladder grind a few generations ahead of the game.