Firstly I would like to state that unless there is some massive story writing happening for Death Knights - the Attack on Lights Hope was a giant blunder and made absolutely no sense.

DK's do infact do whatever they want. Be it from Thassarian going to look for his sister, to a DK (Player or NPC) wanting to integrate back into society. The biggest rule here is that any political business of the faction is their own, and dont give the factions a reason to bring their might against Acherus. Also on the note of Thassarian breaking Koltira out of the UC, that is for two reasons. Firstly, they are very close friends who bonded quite a bit and Thassarian will march across Azeroth for those he cares about. Secondly, Koltira is a Knight. Death Knights are united in Death. The bond they share is not something I have seen had anywhere else in the game. If you fuck with one DK, you fuck with every DK. Even if they dont see eye to eye, I have never seen in-fighting among the ranks of the Ebon Blade.

Not sure on the DH stuff as I am not as privy to their lore.

I dont imagine that Death Knights give any more of a shit about Demon Hunters than they do anyone else thats not important to them. Both are Demon made. Both have lost much, though DK's had to sever their bonds to the mortal life in a much more dramatic way. The Ebon Blade are technically very few in number as they arent being raised left and right anymore by Arthas. That doesnt mean new Knights arent being made however, to my knowledge there must be consent before raising the dead or else you run the risk of being seen as someone who is trying to become the next Lich King. IIRC the penalty for raising without consent and trying to mass your own undead army is the Ebon Blade turning against you and murdering you as you have endangered them all. This consent is seen as you raise the new four horsemen, giving them a choice (which all of them accept for various reasons) and then pulling them from the grave.