Personally, I see little issue in the Southern Water tribe having a chieftain. There's nothing to be lost in merely having an official title for a person whom is already looked upon with widespread approval for his leadership abilities.
Your second paragraph, for me.. requires a lot of perspective. Sure, spirits and humans were at each others' throats (barring Air Nomads), however, it kept most of the human populaces bonded together under the mutual desire for survival. As twisted as it may seem, humans would really have had to either learn to cope with their spiritual neighbors, sequester themselves in villages, or die. Essentially, I don't feel that there would've been any particularly large conflicts between both spirits and humans. Of course, this is when comparing some of the known trials that previous avatars have had to deal with. For example, the Fire Nation essentially wiped out an entire culture and its people, brought dragons to the point of being almost extinct, enslaved all the water benders from the Southern Tribe, and were on the verge of incinerating everything that got in their way. There's also Chin the Conqueror, who desired to put everything, including the avatar, in an inferior position to himself. He too got quite far in his endeavors. I suppose what I'm really trying to say is that I don't think spirits v. humans would've been as bad as humans v. humans. Humans are truly monsters when it comes down to it.
As for your last paragraph, I believe the answer is no. If the present avatar is killed whilst in the avatar state, then the cycle is ended and there is no means of reestablishing it, at least not without the harmonic convergence. When Unalaq merged with Vaatu and took on that demonic form.. I think it transcended the nature of the avatar spirit and would likely lead to the same result. Had Unalaq died without being in that state, then I'd say "yes" is the more practical possibility.