There is a few books around about the history of Dragon Slayers and Dragon Knight with a bit more information. According to me, it's a kind of elite warrior class, but also a sectarian-tendancy order. If I remember well, the first dragon slayers were from the noblety, but it's maybe not the case anymore. It has little importance since they don't remember their familly.
Yes you have the right to kill (as far as you don't get killed back ;)), Rhode is theorically your hierarchically superior but she tends to neglect you when a dragon is around... Dragon Slayers only answer to their own autority, but they must anyway obey the law of local autority (Rhode is going to discover it soon or later :P).
There is two other elite warrior faction: the Champions of Aleroth (like Richard) and the Seekers of Rivertown (there is a bunch of them in Brokenvalley). Basically they both claim themselves as the legacy of the Divine One, but they differ someway in their phylosophy. They are in full concurency.
About politics, in Divine Divinity Aleroth and Rivertown were part of Dukedom of Ferol. However, the last Duke die in the end, so I guess the political scene changed. We meet the rulers of Aleroth (an Archmage and a Champion), but not those of Rivertown so I don't know how it works over there. Far East, there is also Verdistis, a big merchant-ruled city you cannot reach in Divinity II. Far West, in Broken Valley and Orobas Fjord, it's mostly wild, so I would say town watch and seeker basement are the highest autority - not to mention bandits.
About races, you won't meet a lot of peacefully non-human species. At least no elves and dwarves anymore, since they hide themselves (according to some books). In Divine Divinity, I would say those races were even more egalitarian than humans (all their females could actually fight, and fight quite well). Anyway, in Divinity II there is only goblins, and I didn't notice any female NPC amount them.
Well, I hope I answered all your questions
