Faction elimination:
This is my experience: I had the same problem after I took all of the Khergit towns, castles and villages. The faction didn't cease to exist immediately. At first I thought it was impossible to totally eliminate a faction, but when I continued to conquer the other factions I would find small bands of Khergits roaming the countryside and usually run away from me (which they actually can with their all-cavalry forces despite my movement speed bonus). At times they would try to raid villages in poorly defended areas. That is when I decided to "bait" them by leaving a castle without a garrison, and sure enough the last three vassals of the Khergits each tried to take it. With a cavalry-only army I was able to hunt them down. After that I got a very clear but unceremonious message stating that the Khergit Khanaate had ceased to exist as a faction. I shared your disappointment in that no one really seemed to notice or care about it at all. A simple: "Good job, my boy!" from the king would have gone a long way.
Invisible ladies:
Titan357 said all there is to it. You can only interact the ladies after you have met them at a feast, or by asking permission to visit her from her family. I think this makes sense since women in those times weren't allowed to wander around, and their families kept them on a short leash. Don't elope with a lady unless she belongs to an enemy faction or if it's impossible to get in her father's good graces! I did it, and it didn't just cause trouble with the father as I expected, but also the father's friends and even the king himself gave me a big relationship hit.